Sufficient conditions for supersolubility of finite groups
type: Item
instance of: scholarly article
title: Sufficient conditions for supersolubility of finite groups
zbMATH Open document ID: 0928.20020
DOI: 10.1016/S0022-4049(96)00172-7
published in: Journal of Pure and Applied Algebra
publication date: 2000-01-16T00:00:00Z
review text: A subgroup \(H\) of a finite group \(G\) is \(S\)-quasinormal in \(G\) if it permutes with each Sylow subgroup of \(G\); a subgroup \(K\) of \(G\) is \(S\)-quasinormally embedded in \(G\) if each Sylow subgroup of \(K\) is also a Sylow subgroup of some \(S\)-quasinormal subgroup of \(G\). The authors prove: Theorem 1. If each maximal subgroup of the Sylow subgroups of \(G\) is \(S\)-quasinormally embedded in \(G\), then \(G\) is supersolvable. Theorem 2. If \(G\) is a solvable group with normal subgroup \(H\) such that \(G/H\) is supersolvable and all maximal subgroups of the Sylow subgroups of the Fitting subgroup of \(H\) are \(S\)-quasinormally embedded in \(G\), then \(G\) is supersolvable.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 1308160
zbMATH Keywords: finite groups
zbMATH Keywords: quasinormal subgroups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: supersolvable groups
zbMATH Keywords: solvable groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: Fitting subgroups
author: Adolfo Ballester-Bolinches
author: Mari Carmen Pedraza-Aguilera
reviewed by: W. E. Deskins
MaRDI profile type: Publication
cites work: Influence of \(\pi\)-quasinormality on maximal subgroups of Sylow subgroups of Fitting subgroup of a finite group
cites work: Permutably embedded subgroups of finite soluble groups
cites work: On quasinormal subgroups of finite groups
cites work: Finite soluble groups
cites work: Sylow-Gruppen und Subnormalteiler endlicher Gruppen
cites work: Two sufficient conditions for supersolvability of finite groups
full work available at URL: s0022-4049(96)00172-7
OpenAlex ID: W2106899941
description: scientific article; zbMATH DE number 1308160