Nilpotent length and system permutability
If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup...
Ausführliche Beschreibung
Autor*in: |
Dark, Rex [verfasserIn] Feldman, Arnold D. [verfasserIn] Pérez-Ramos, María Dolores [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch |
Erschienen: |
2021 |
---|
Schlagwörter: |
---|
Übergeordnetes Werk: |
Enthalten in: Journal of algebra - San Diego, Calif. : Elsevier, 1964, 589, Seite 287-322 |
---|---|
Übergeordnetes Werk: |
volume:589 ; pages:287-322 |
DOI / URN: |
10.1016/j.jalgebra.2021.08.028 |
---|
Katalog-ID: |
ELV006785638 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | ELV006785638 | ||
003 | DE-627 | ||
005 | 20230524131332.0 | ||
007 | cr uuu---uuuuu | ||
008 | 230506s2021 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.1016/j.jalgebra.2021.08.028 |2 doi | |
035 | |a (DE-627)ELV006785638 | ||
035 | |a (ELSEVIER)S0021-8693(21)00457-9 | ||
040 | |a DE-627 |b ger |c DE-627 |e rda | ||
041 | |a eng | ||
082 | 0 | 4 | |a 510 |q DE-600 |
084 | |a 31.20 |2 bkl | ||
100 | 1 | |a Dark, Rex |e verfasserin |0 (orcid)0000-0002-4207-2323 |4 aut | |
245 | 1 | 0 | |a Nilpotent length and system permutability |
264 | 1 | |c 2021 | |
336 | |a nicht spezifiziert |b zzz |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
520 | |a If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. | ||
650 | 4 | |a Finite soluble group | |
650 | 4 | |a Fitting class | |
650 | 4 | |a Injector | |
650 | 4 | |a System permutability | |
700 | 1 | |a Feldman, Arnold D. |e verfasserin |4 aut | |
700 | 1 | |a Pérez-Ramos, María Dolores |e verfasserin |0 (orcid)0000-0003-0173-2759 |4 aut | |
773 | 0 | 8 | |i Enthalten in |t Journal of algebra |d San Diego, Calif. : Elsevier, 1964 |g 589, Seite 287-322 |h Online-Ressource |w (DE-627)266890423 |w (DE-600)1468947-9 |w (DE-576)10337311X |x 1090-266X |7 nnns |
773 | 1 | 8 | |g volume:589 |g pages:287-322 |
912 | |a GBV_USEFLAG_U | ||
912 | |a SYSFLAG_U | ||
912 | |a GBV_ELV | ||
912 | |a SSG-OPC-MAT | ||
912 | |a GBV_ILN_20 | ||
912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_23 | ||
912 | |a GBV_ILN_24 | ||
912 | |a GBV_ILN_31 | ||
912 | |a GBV_ILN_32 | ||
912 | |a GBV_ILN_40 | ||
912 | |a GBV_ILN_60 | ||
912 | |a GBV_ILN_62 | ||
912 | |a GBV_ILN_63 | ||
912 | |a GBV_ILN_69 | ||
912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_73 | ||
912 | |a GBV_ILN_74 | ||
912 | |a GBV_ILN_90 | ||
912 | |a GBV_ILN_95 | ||
912 | |a GBV_ILN_100 | ||
912 | |a GBV_ILN_105 | ||
912 | |a GBV_ILN_110 | ||
912 | |a GBV_ILN_150 | ||
912 | |a GBV_ILN_151 | ||
912 | |a GBV_ILN_224 | ||
912 | |a GBV_ILN_370 | ||
912 | |a GBV_ILN_602 | ||
912 | |a GBV_ILN_702 | ||
912 | |a GBV_ILN_2003 | ||
912 | |a GBV_ILN_2004 | ||
912 | |a GBV_ILN_2005 | ||
912 | |a GBV_ILN_2011 | ||
912 | |a GBV_ILN_2014 | ||
912 | |a GBV_ILN_2015 | ||
912 | |a GBV_ILN_2020 | ||
912 | |a GBV_ILN_2021 | ||
912 | |a GBV_ILN_2025 | ||
912 | |a GBV_ILN_2027 | ||
912 | |a GBV_ILN_2034 | ||
912 | |a GBV_ILN_2038 | ||
912 | |a GBV_ILN_2044 | ||
912 | |a GBV_ILN_2048 | ||
912 | |a GBV_ILN_2049 | ||
912 | |a GBV_ILN_2050 | ||
912 | |a GBV_ILN_2056 | ||
912 | |a GBV_ILN_2059 | ||
912 | |a GBV_ILN_2061 | ||
912 | |a GBV_ILN_2064 | ||
912 | |a GBV_ILN_2065 | ||
912 | |a GBV_ILN_2068 | ||
912 | |a GBV_ILN_2111 | ||
912 | |a GBV_ILN_2112 | ||
912 | |a GBV_ILN_2113 | ||
912 | |a GBV_ILN_2118 | ||
912 | |a GBV_ILN_2122 | ||
912 | |a GBV_ILN_2129 | ||
912 | |a GBV_ILN_2143 | ||
912 | |a GBV_ILN_2147 | ||
912 | |a GBV_ILN_2148 | ||
912 | |a GBV_ILN_2152 | ||
912 | |a GBV_ILN_2153 | ||
912 | |a GBV_ILN_2190 | ||
912 | |a GBV_ILN_2336 | ||
912 | |a GBV_ILN_2507 | ||
912 | |a GBV_ILN_2522 | ||
912 | |a GBV_ILN_4012 | ||
912 | |a GBV_ILN_4035 | ||
912 | |a GBV_ILN_4037 | ||
912 | |a GBV_ILN_4112 | ||
912 | |a GBV_ILN_4125 | ||
912 | |a GBV_ILN_4126 | ||
912 | |a GBV_ILN_4242 | ||
912 | |a GBV_ILN_4249 | ||
912 | |a GBV_ILN_4251 | ||
912 | |a GBV_ILN_4305 | ||
912 | |a GBV_ILN_4306 | ||
912 | |a GBV_ILN_4307 | ||
912 | |a GBV_ILN_4313 | ||
912 | |a GBV_ILN_4322 | ||
912 | |a GBV_ILN_4323 | ||
912 | |a GBV_ILN_4324 | ||
912 | |a GBV_ILN_4325 | ||
912 | |a GBV_ILN_4326 | ||
912 | |a GBV_ILN_4333 | ||
912 | |a GBV_ILN_4334 | ||
912 | |a GBV_ILN_4335 | ||
912 | |a GBV_ILN_4338 | ||
912 | |a GBV_ILN_4367 | ||
912 | |a GBV_ILN_4393 | ||
912 | |a GBV_ILN_4700 | ||
936 | b | k | |a 31.20 |j Algebra: Allgemeines |
951 | |a AR | ||
952 | |d 589 |h 287-322 |
author_variant |
r d rd a d f ad adf m d p r mdp mdpr |
---|---|
matchkey_str |
article:1090266X:2021----::iptnlntadytme |
hierarchy_sort_str |
2021 |
bklnumber |
31.20 |
publishDate |
2021 |
allfields |
10.1016/j.jalgebra.2021.08.028 doi (DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Dark, Rex verfasserin (orcid)0000-0002-4207-2323 aut Nilpotent length and system permutability 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. Finite soluble group Fitting class Injector System permutability Feldman, Arnold D. verfasserin aut Pérez-Ramos, María Dolores verfasserin (orcid)0000-0003-0173-2759 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 589, Seite 287-322 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:589 pages:287-322 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 589 287-322 |
spelling |
10.1016/j.jalgebra.2021.08.028 doi (DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Dark, Rex verfasserin (orcid)0000-0002-4207-2323 aut Nilpotent length and system permutability 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. Finite soluble group Fitting class Injector System permutability Feldman, Arnold D. verfasserin aut Pérez-Ramos, María Dolores verfasserin (orcid)0000-0003-0173-2759 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 589, Seite 287-322 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:589 pages:287-322 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 589 287-322 |
allfields_unstemmed |
10.1016/j.jalgebra.2021.08.028 doi (DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Dark, Rex verfasserin (orcid)0000-0002-4207-2323 aut Nilpotent length and system permutability 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. Finite soluble group Fitting class Injector System permutability Feldman, Arnold D. verfasserin aut Pérez-Ramos, María Dolores verfasserin (orcid)0000-0003-0173-2759 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 589, Seite 287-322 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:589 pages:287-322 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 589 287-322 |
allfieldsGer |
10.1016/j.jalgebra.2021.08.028 doi (DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Dark, Rex verfasserin (orcid)0000-0002-4207-2323 aut Nilpotent length and system permutability 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. Finite soluble group Fitting class Injector System permutability Feldman, Arnold D. verfasserin aut Pérez-Ramos, María Dolores verfasserin (orcid)0000-0003-0173-2759 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 589, Seite 287-322 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:589 pages:287-322 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 589 287-322 |
allfieldsSound |
10.1016/j.jalgebra.2021.08.028 doi (DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 DE-627 ger DE-627 rda eng 510 DE-600 31.20 bkl Dark, Rex verfasserin (orcid)0000-0002-4207-2323 aut Nilpotent length and system permutability 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. Finite soluble group Fitting class Injector System permutability Feldman, Arnold D. verfasserin aut Pérez-Ramos, María Dolores verfasserin (orcid)0000-0003-0173-2759 aut Enthalten in Journal of algebra San Diego, Calif. : Elsevier, 1964 589, Seite 287-322 Online-Ressource (DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X 1090-266X nnns volume:589 pages:287-322 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.20 Algebra: Allgemeines AR 589 287-322 |
language |
English |
source |
Enthalten in Journal of algebra 589, Seite 287-322 volume:589 pages:287-322 |
sourceStr |
Enthalten in Journal of algebra 589, Seite 287-322 volume:589 pages:287-322 |
format_phy_str_mv |
Article |
bklname |
Algebra: Allgemeines |
institution |
findex.gbv.de |
topic_facet |
Finite soluble group Fitting class Injector System permutability |
dewey-raw |
510 |
isfreeaccess_bool |
false |
container_title |
Journal of algebra |
authorswithroles_txt_mv |
Dark, Rex @@aut@@ Feldman, Arnold D. @@aut@@ Pérez-Ramos, María Dolores @@aut@@ |
publishDateDaySort_date |
2021-01-01T00:00:00Z |
hierarchy_top_id |
266890423 |
dewey-sort |
3510 |
id |
ELV006785638 |
language_de |
englisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV006785638</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524131332.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230506s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jalgebra.2021.08.028</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV006785638</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0021-8693(21)00457-9</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.20</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dark, Rex</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-4207-2323</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nilpotent length and system permutability</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite soluble group</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fitting class</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Injector</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">System permutability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feldman, Arnold D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pérez-Ramos, María Dolores</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0173-2759</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of algebra</subfield><subfield code="d">San Diego, Calif. : Elsevier, 1964</subfield><subfield code="g">589, Seite 287-322</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)266890423</subfield><subfield code="w">(DE-600)1468947-9</subfield><subfield code="w">(DE-576)10337311X</subfield><subfield code="x">1090-266X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:589</subfield><subfield code="g">pages:287-322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.20</subfield><subfield code="j">Algebra: Allgemeines</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">589</subfield><subfield code="h">287-322</subfield></datafield></record></collection>
|
author |
Dark, Rex |
spellingShingle |
Dark, Rex ddc 510 bkl 31.20 misc Finite soluble group misc Fitting class misc Injector misc System permutability Nilpotent length and system permutability |
authorStr |
Dark, Rex |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)266890423 |
format |
electronic Article |
dewey-ones |
510 - Mathematics |
delete_txt_mv |
keep |
author_role |
aut aut aut |
collection |
elsevier |
remote_str |
true |
illustrated |
Not Illustrated |
issn |
1090-266X |
topic_title |
510 DE-600 31.20 bkl Nilpotent length and system permutability Finite soluble group Fitting class Injector System permutability |
topic |
ddc 510 bkl 31.20 misc Finite soluble group misc Fitting class misc Injector misc System permutability |
topic_unstemmed |
ddc 510 bkl 31.20 misc Finite soluble group misc Fitting class misc Injector misc System permutability |
topic_browse |
ddc 510 bkl 31.20 misc Finite soluble group misc Fitting class misc Injector misc System permutability |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
Journal of algebra |
hierarchy_parent_id |
266890423 |
dewey-tens |
510 - Mathematics |
hierarchy_top_title |
Journal of algebra |
isfreeaccess_txt |
false |
familylinks_str_mv |
(DE-627)266890423 (DE-600)1468947-9 (DE-576)10337311X |
title |
Nilpotent length and system permutability |
ctrlnum |
(DE-627)ELV006785638 (ELSEVIER)S0021-8693(21)00457-9 |
title_full |
Nilpotent length and system permutability |
author_sort |
Dark, Rex |
journal |
Journal of algebra |
journalStr |
Journal of algebra |
lang_code |
eng |
isOA_bool |
false |
dewey-hundreds |
500 - Science |
recordtype |
marc |
publishDateSort |
2021 |
contenttype_str_mv |
zzz |
container_start_page |
287 |
author_browse |
Dark, Rex Feldman, Arnold D. Pérez-Ramos, María Dolores |
container_volume |
589 |
class |
510 DE-600 31.20 bkl |
format_se |
Elektronische Aufsätze |
author-letter |
Dark, Rex |
doi_str_mv |
10.1016/j.jalgebra.2021.08.028 |
normlink |
(ORCID)0000-0002-4207-2323 (ORCID)0000-0003-0173-2759 |
normlink_prefix_str_mv |
(orcid)0000-0002-4207-2323 (orcid)0000-0003-0173-2759 |
dewey-full |
510 |
author2-role |
verfasserin |
title_sort |
nilpotent length and system permutability |
title_auth |
Nilpotent length and system permutability |
abstract |
If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. |
abstractGer |
If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. |
abstract_unstemmed |
If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible. |
collection_details |
GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 |
title_short |
Nilpotent length and system permutability |
remote_bool |
true |
author2 |
Feldman, Arnold D. Pérez-Ramos, María Dolores |
author2Str |
Feldman, Arnold D. Pérez-Ramos, María Dolores |
ppnlink |
266890423 |
mediatype_str_mv |
c |
isOA_txt |
false |
hochschulschrift_bool |
false |
doi_str |
10.1016/j.jalgebra.2021.08.028 |
up_date |
2024-07-06T22:33:26.725Z |
_version_ |
1803870752448970752 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">ELV006785638</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230524131332.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230506s2021 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1016/j.jalgebra.2021.08.028</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)ELV006785638</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ELSEVIER)S0021-8693(21)00457-9</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">31.20</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dark, Rex</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-4207-2323</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nilpotent length and system permutability</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">nicht spezifiziert</subfield><subfield code="b">zzz</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">If C is a class of groups, a C -injector of a finite group G is a subgroup V of G with the property that V ∩ K is a C -maximal subgroup of K for all subnormal subgroups K of G. The classical result of B. Fischer, W. Gaschütz and B. Hartley states the existence and conjugacy of F -injectors in finite soluble groups for Fitting classes F . We shall show that for groups of nilpotent length at most 4, F -injectors permute with the members of a Sylow basis in the group. We shall exhibit the construction of a Fitting class and a group of nilpotent length 5, which fail to satisfy the result and show that the bound is the best possible.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite soluble group</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fitting class</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Injector</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">System permutability</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Feldman, Arnold D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Pérez-Ramos, María Dolores</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0173-2759</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of algebra</subfield><subfield code="d">San Diego, Calif. : Elsevier, 1964</subfield><subfield code="g">589, Seite 287-322</subfield><subfield code="h">Online-Ressource</subfield><subfield code="w">(DE-627)266890423</subfield><subfield code="w">(DE-600)1468947-9</subfield><subfield code="w">(DE-576)10337311X</subfield><subfield code="x">1090-266X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:589</subfield><subfield code="g">pages:287-322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ELV</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="936" ind1="b" ind2="k"><subfield code="a">31.20</subfield><subfield code="j">Algebra: Allgemeines</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">589</subfield><subfield code="h">287-322</subfield></datafield></record></collection>
|
score |
7.400199 |