Periodic linear groups in which permutability is a transitive relation

Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Syl...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Ferrara, Maria [verfasserIn] Trombetti, Marco

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Linear group -group Fusion theory Pronormal subgroup Graph

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Annali di matematica pura ed applicata - Berlin : Springer, 1858, 203(2023), 1 vom: 28. Aug., Seite 361-383
Übergeordnetes Werk:	volume:203 ; year:2023 ; number:1 ; day:28 ; month:08 ; pages:361-383

Links:	Volltext

DOI / URN:	10.1007/s10231-023-01367-2

Katalog-ID:	SPR054290910

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520			\|a Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups.
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allfields	10.1007/s10231-023-01367-2 doi (DE-627)SPR054290910 (SPR)s10231-023-01367-2-e DE-627 ger DE-627 rakwb eng Ferrara, Maria verfasserin aut Periodic linear groups in which permutability is a transitive relation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213 Trombetti, Marco (orcid)0000-0003-4532-3690 aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 203(2023), 1 vom: 28. Aug., Seite 361-383 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:203 year:2023 number:1 day:28 month:08 pages:361-383 https://dx.doi.org/10.1007/s10231-023-01367-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 203 2023 1 28 08 361-383
spelling	10.1007/s10231-023-01367-2 doi (DE-627)SPR054290910 (SPR)s10231-023-01367-2-e DE-627 ger DE-627 rakwb eng Ferrara, Maria verfasserin aut Periodic linear groups in which permutability is a transitive relation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213 Trombetti, Marco (orcid)0000-0003-4532-3690 aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 203(2023), 1 vom: 28. Aug., Seite 361-383 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:203 year:2023 number:1 day:28 month:08 pages:361-383 https://dx.doi.org/10.1007/s10231-023-01367-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 203 2023 1 28 08 361-383
allfields_unstemmed	10.1007/s10231-023-01367-2 doi (DE-627)SPR054290910 (SPR)s10231-023-01367-2-e DE-627 ger DE-627 rakwb eng Ferrara, Maria verfasserin aut Periodic linear groups in which permutability is a transitive relation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213 Trombetti, Marco (orcid)0000-0003-4532-3690 aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 203(2023), 1 vom: 28. Aug., Seite 361-383 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:203 year:2023 number:1 day:28 month:08 pages:361-383 https://dx.doi.org/10.1007/s10231-023-01367-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 203 2023 1 28 08 361-383
allfieldsGer	10.1007/s10231-023-01367-2 doi (DE-627)SPR054290910 (SPR)s10231-023-01367-2-e DE-627 ger DE-627 rakwb eng Ferrara, Maria verfasserin aut Periodic linear groups in which permutability is a transitive relation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213 Trombetti, Marco (orcid)0000-0003-4532-3690 aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 203(2023), 1 vom: 28. Aug., Seite 361-383 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:203 year:2023 number:1 day:28 month:08 pages:361-383 https://dx.doi.org/10.1007/s10231-023-01367-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 203 2023 1 28 08 361-383
allfieldsSound	10.1007/s10231-023-01367-2 doi (DE-627)SPR054290910 (SPR)s10231-023-01367-2-e DE-627 ger DE-627 rakwb eng Ferrara, Maria verfasserin aut Periodic linear groups in which permutability is a transitive relation 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213 Trombetti, Marco (orcid)0000-0003-4532-3690 aut Enthalten in Annali di matematica pura ed applicata Berlin : Springer, 1858 203(2023), 1 vom: 28. Aug., Seite 361-383 (DE-627)330615289 (DE-600)2049996-6 1618-1891 nnns volume:203 year:2023 number:1 day:28 month:08 pages:361-383 https://dx.doi.org/10.1007/s10231-023-01367-2 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER 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_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_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_2118 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 203 2023 1 28 08 361-383
language	English
source	Enthalten in Annali di matematica pura ed applicata 203(2023), 1 vom: 28. Aug., Seite 361-383 volume:203 year:2023 number:1 day:28 month:08 pages:361-383
sourceStr	Enthalten in Annali di matematica pura ed applicata 203(2023), 1 vom: 28. Aug., Seite 361-383 volume:203 year:2023 number:1 day:28 month:08 pages:361-383
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Linear group -group Fusion theory Pronormal subgroup Graph
isfreeaccess_bool	true
container_title	Annali di matematica pura ed applicata
authorswithroles_txt_mv	Ferrara, Maria @@aut@@ Trombetti, Marco @@aut@@
publishDateDaySort_date	2023-08-28T00:00:00Z
hierarchy_top_id	330615289
id	SPR054290910
language_de	englisch
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The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). 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author	Ferrara, Maria
spellingShingle	Ferrara, Maria misc Linear group misc -group misc Fusion theory misc Pronormal subgroup misc Graph Periodic linear groups in which permutability is a transitive relation
authorStr	Ferrara, Maria
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topic_title	Periodic linear groups in which permutability is a transitive relation Linear group (dpeaa)DE-He213 -group (dpeaa)DE-He213 Fusion theory (dpeaa)DE-He213 Pronormal subgroup (dpeaa)DE-He213 Graph (dpeaa)DE-He213
topic	misc Linear group misc -group misc Fusion theory misc Pronormal subgroup misc Graph
topic_unstemmed	misc Linear group misc -group misc Fusion theory misc Pronormal subgroup misc Graph
topic_browse	misc Linear group misc -group misc Fusion theory misc Pronormal subgroup misc Graph
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title	Periodic linear groups in which permutability is a transitive relation
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title_full	Periodic linear groups in which permutability is a transitive relation
author_sort	Ferrara, Maria
journal	Annali di matematica pura ed applicata
journalStr	Annali di matematica pura ed applicata
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author_browse	Ferrara, Maria Trombetti, Marco
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author-letter	Ferrara, Maria
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title_sort	periodic linear groups in which permutability is a transitive relation
title_auth	Periodic linear groups in which permutability is a transitive relation
abstract	Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. © The Author(s) 2023
abstractGer	Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. © The Author(s) 2023
abstract_unstemmed	Abstract A PT-group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic image of a) periodic linear group is a soluble PT-group if and only if each subgroup of a Sylow subgroup is permutable in the corresponding Sylow normalizer (see Theorem 4.7); for a fixed prime p, the latter condition is denoted by %$\mathfrak {X}_p%$. In order to prove our main theorem, we need (i) to characterize (homomorphic images of) periodic linear groups that are PT-groups (see Sect. 2), (ii) to develop a fusion theory for locally finite groups (see Sect. 3), (iii) to carefully study (homomorphic images of) periodic linear groups with the property %$\mathfrak {X}_p%$ for a fixed prime p (see for instance Theorem 4.6). As a by-product we obtain (among other results) a characterization of (homomorphic images of) periodic linear %$\mathfrak {X}_p%$-groups in terms of pronormality (see Theorem 4.11) that will allow us to show that, on some occasions, the property %$\mathfrak {X}_p%$ is inherited by subgroups. © The Author(s) 2023
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title_short	Periodic linear groups in which permutability is a transitive relation
url	https://dx.doi.org/10.1007/s10231-023-01367-2
remote_bool	true
author2	Trombetti, Marco
author2Str	Trombetti, Marco
ppnlink	330615289
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doi_str	10.1007/s10231-023-01367-2
up_date	2024-07-04T00:54:07.254Z
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score	7.400324

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Periodic linear groups in which permutability is a transitive relation

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