Finite π-groups with normal injectors

Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal F...
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Autor*in:	Vorob’ev, N. T. [verfasserIn] Martsinkevich, A. V. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes

Übergeordnetes Werk:	Enthalten in: Siberian mathematical journal - New York, NY [u.a.] : Consultants Bureau, 1966, 56(2015), 4 vom: Juli, Seite 624-630
Übergeordnetes Werk:	volume:56 ; year:2015 ; number:4 ; month:07 ; pages:624-630

Links:	Volltext

DOI / URN:	10.1134/S0037446615040060

Katalog-ID:	SPR017689031

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520			\|a Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes.
650		4	\|a Fitting class \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_73
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912			\|a GBV_ILN_161
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912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
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912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
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912			\|a GBV_ILN_602
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912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
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912			\|a GBV_ILN_2050
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912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
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allfields	10.1134/S0037446615040060 doi (DE-627)SPR017689031 (SPR)S0037446615040060-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213 Martsinkevich, A. V. verfasserin aut Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://dx.doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 56 2015 4 07 624-630
spelling	10.1134/S0037446615040060 doi (DE-627)SPR017689031 (SPR)S0037446615040060-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213 Martsinkevich, A. V. verfasserin aut Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://dx.doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 56 2015 4 07 624-630
allfields_unstemmed	10.1134/S0037446615040060 doi (DE-627)SPR017689031 (SPR)S0037446615040060-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213 Martsinkevich, A. V. verfasserin aut Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://dx.doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 56 2015 4 07 624-630
allfieldsGer	10.1134/S0037446615040060 doi (DE-627)SPR017689031 (SPR)S0037446615040060-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213 Martsinkevich, A. V. verfasserin aut Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://dx.doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 56 2015 4 07 624-630
allfieldsSound	10.1134/S0037446615040060 doi (DE-627)SPR017689031 (SPR)S0037446615040060-e DE-627 ger DE-627 rakwb eng 510 ASE 31.00 bkl Vorob’ev, N. T. verfasserin aut Finite π-groups with normal injectors 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes. Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213 Martsinkevich, A. V. verfasserin aut Enthalten in Siberian mathematical journal New York, NY [u.a.] : Consultants Bureau, 1966 56(2015), 4 vom: Juli, Seite 624-630 (DE-627)325572348 (DE-600)2037555-4 1573-9260 nnns volume:56 year:2015 number:4 month:07 pages:624-630 https://dx.doi.org/10.1134/S0037446615040060 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 ASE AR 56 2015 4 07 624-630
language	English
source	Enthalten in Siberian mathematical journal 56(2015), 4 vom: Juli, Seite 624-630 volume:56 year:2015 number:4 month:07 pages:624-630
sourceStr	Enthalten in Siberian mathematical journal 56(2015), 4 vom: Juli, Seite 624-630 volume:56 year:2015 number:4 month:07 pages:624-630
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Fitting class π-normal Fitting class product of Fitting classes lattice join of Fitting classes
dewey-raw	510
isfreeaccess_bool	false
container_title	Siberian mathematical journal
authorswithroles_txt_mv	Vorob’ev, N. T. @@aut@@ Martsinkevich, A. V. @@aut@@
publishDateDaySort_date	2015-07-01T00:00:00Z
hierarchy_top_id	325572348
dewey-sort	3510
id	SPR017689031
language_de	englisch
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author	Vorob’ev, N. T.
spellingShingle	Vorob’ev, N. T. ddc 510 bkl 31.00 misc Fitting class misc π-normal Fitting class misc product of Fitting classes misc lattice join of Fitting classes Finite π-groups with normal injectors
authorStr	Vorob’ev, N. T.
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topic_title	510 ASE 31.00 bkl Finite π-groups with normal injectors Fitting class (dpeaa)DE-He213 π-normal Fitting class (dpeaa)DE-He213 product of Fitting classes (dpeaa)DE-He213 lattice join of Fitting classes (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc Fitting class misc π-normal Fitting class misc product of Fitting classes misc lattice join of Fitting classes
topic_unstemmed	ddc 510 bkl 31.00 misc Fitting class misc π-normal Fitting class misc product of Fitting classes misc lattice join of Fitting classes
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title	Finite π-groups with normal injectors
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title_full	Finite π-groups with normal injectors
author_sort	Vorob’ev, N. T.
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author_browse	Vorob’ev, N. T. Martsinkevich, A. V.
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title_sort	finite π-groups with normal injectors
title_auth	Finite π-groups with normal injectors
abstract	Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes.
abstractGer	Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes.
abstract_unstemmed	Abstract Denote by P the set of all primes and take a nonempty set π ⊆ P. A Fitting class F ≠ (1) is called normal in the class Sπ of all finite soluble π-groups or π-normal, whenever F ⊆ Sπ and for every G ∈ Sπ its F-injectors constitute a normal subgroup of G. We study the properties of π-normal Fitting classes. Using Lockett operators, we prove a criterion for the π-normality of products of Fitting classes. A π-normal Fitting class is normal in the case π = P. The lattice of all solvable normal Fitting classes is a sublattice of the lattice of all solvable Fitting classes; but the question of modularity of the lattice of all solvable Fitting classes is open (see Question 14.47 in [1]). We obtain a positive answer to a similar question in the case of π-normal Fitting classes.
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container_issue	4
title_short	Finite π-groups with normal injectors
url	https://dx.doi.org/10.1134/S0037446615040060
remote_bool	true
author2	Martsinkevich, A. V.
author2Str	Martsinkevich, A. V.
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hochschulschrift_bool	false
doi_str	10.1134/S0037446615040060
up_date	2024-07-03T14:31:52.883Z
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score	7.401636

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Finite π-groups with normal injectors

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