Influence of normality on maximal subgroups of Sylow subgroups of a finite group
type: Item
instance of: scholarly article
title: Influence of normality on maximal subgroups of Sylow subgroups of a finite group
zbMATH Open document ID: 0802.20019
DOI: 10.1007/BF00052096
author: S. Singh
published in: Acta Mathematica Hungarica
publication date: 1993-04-01T00:00:00Z
review text: This paper deals with the influence of the normality of the maximal subgroups of Sylow \(p\)-subgroups of a finite group \(G\) on the structure of \(G\). Here is a sample of the results obtained: 1) If \(G\) is a finite solvable group and every maximal subgroup of the Sylow subgroups of the Fitting subgroup \(F(G)\) is normal in \(G\), then \(G\) is supersolvable. 2) Let \(G\) be a finite group, let \(H \triangleleft G\) and assume that \(G/H\) is supersolvable and all maximal subgroups of the Sylow subgroups of \(H\) are normal in \(G\). Then \(G\) is supersolvable. 3) Let \(G\) be a finite group, let \(p = \max(\pi(G))\) and assume that every maximal subgroup of the Sylow \(q\)-subgroups of \(G\) is normal in \(G\) for all \(q \in \pi(G) - \{p\}\). Then \(G\) has a Sylow tower and \(G/O_ p(G)\) is supersolvable. In particular, \(G\) is solvable.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 149654
zbMATH Keywords: supersolvable groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: Sylow \(p\)-subgroups
zbMATH Keywords: finite group
zbMATH Keywords: finite solvable group
zbMATH Keywords: Fitting subgroup
zbMATH Keywords: Sylow tower
reviewed by: Marian Deaconescu
MaRDI profile type: Publication
cites work: Endliche Gruppen I
cites work: Q5577154
cites work: Q4146884
cites work: Supersoluble Immersion
cites work: Two sufficient conditions for supersolvability of finite groups
cites work: Q5331572
description: scientific article; zbMATH DE number 149654