The influence of \(c\)-normality of subgroups on the structure of finite groups
type: Item
instance of: scholarly article
title: The influence of \(c\)-normality of subgroups on the structure of finite groups
zbMATH Open document ID: 0967.20011
DOI: 10.1016/S0022-4049(99)00042-0
published in: Journal of Pure and Applied Algebra
publication date: 2001-05-28T00:00:00Z
review text: A subgroup \(H\) of a finite group \(G\) is \(c\)-normal if there is a normal subgroup \(G>N\) such that \(HN=G\) and \(H\cap N\) lies in the core of \(H\). The authors investigate the influence of \(c\)-normality on the structure of \(G\), obtaining, for example, the following result on supersolvability. If \(N\) is a normal subgroup of \(G\) such that (1) \(G/N\) is supersolvable and (2) \(P_1\) is \(c\)-normal in \(G\) for every Sylow subgroup \(P\) of \(N\) and every maximal subgroup \(P_1\) of \(P\), then \(G\) is supersolvable.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 1488533
zbMATH Keywords: finite groups
zbMATH Keywords: \(c\)-normal subgroups
zbMATH Keywords: supersolvability
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: maximal subgroups
author: Deyu Li
author: Xiuyun Guo
reviewed by: W. E. Deskins
MaRDI profile type: Publication
full work available at URL: s0022-4049(99)00042-0
OpenAlex ID: W2050612484
Wikidata QID: Q126438172
Recommended article: Q4782872
Recommended article: Q4416402
Recommended article: Q3597678
Recommended article: The influence of c-normality of subgroups on the structure of finite groups II*
Recommended article: Q4440784
Recommended article: Q4537683
Recommended article: Q3513476
Recommended article: The influence of nonnormal noncyclic subgroups on the structure of finite groups
Recommended article: On c-normal subgroups of finite groups
Recommended article: On c#-normal subgroups of finite groups
description: scientific article; zbMATH DE number 1488533