Sylow permutable subnormal subgroups of finite groups
type: Item
instance of: scholarly article
title: Sylow permutable subnormal subgroups of finite groups
zbMATH Open document ID: 1010.20013
author: Adolfo Ballester-Bolinches
author: R. Esteban-Romero
published in: Journal of Algebra
publication date: 2002-12-16T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/18473
review text: Let \(p\) be a prime. The authors consider groups \(G\) with modular Sylow \(p\)-subgroup \(S\) and show for this class that \(p\)-nilpotency of \(G\) and \(N_G(S)\) imply each other. Also, \(p\)-subgroups that are permutable with all Sylow subgroups are permutable with all subgroups if \(S\) is modular. If all Sylow subgroups are modular, permutability with all Sylow subgroups implies permutability with all subgroups (Theorems 1 and 2). Implications are given concerning group classes near to PST-groups.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D35
zbMATH DE Number: 1846019
zbMATH Keywords: modular Sylow subgroups
zbMATH Keywords: \(p\)-nilpotency
zbMATH Keywords: permutable subgroups
zbMATH Keywords: PST-groups
reviewed by: Hermann Heineken
describes a project that uses: permut
MaRDI profile type: Publication
OpenAlex ID: W1993964841
cites work: Finite Groups whose Subnormal Subgroups Permute with all Sylow Subgroups
cites work: Finite soluble groups with permutable subnormal subgroups
cites work: Sylow permutable subnormal subgroups of finite groups. II
cites work: Criteria for permutability to be transitive in finite groups
cites work: Finite soluble groups whose subnormal subgroups permute with certain classes of subgroups
cites work: The Wielandt Subgroup of a Finite Soluble Group
cites work: Gruppen, in denen das Normalteilersein transitiv ist.
cites work: Zur Sylowstruktur auflösbarer Gruppen
cites work: Endliche Gruppen I
cites work: Sylow-Gruppen und Subnormalteiler endlicher Gruppen
cites work: A Note on Finite Groups in Which Normality is Transitive
cites work: Q4146884
cites work: Subgroups permutable with all Sylow subgroups
cites work: Subgroup lattices of groups
cites work: Q5510848
cites work: On Two Theorems of Thompson
DOI: 10.1006/JABR.2001.9138
Recommended article: Sylow permutable subnormal subgroups of finite groups. II
Recommended article: On Sylow permutable subgroups of finite groups
Recommended article: Q3033956
Recommended article: Sylow p -Subgroups and Subnormal Subgroups of Finite Groups
Recommended article: Q5193127
Recommended article: Q2956920
Recommended article: Finite groups with \(\mathbb{P} \)-subnormal Sylow subgroups
Recommended article: Permutable subnormal subgroups of finite groups.
Recommended article: Groups in which Sylow subgroups and subnormal subgroups permute.
Recommended article: Finite soluble groups with permutable subnormal subgroups
description: scientific article; zbMATH DE number 1846019