The influence of \(\pi\)-quasinormality of some subgroups of a finite group.
type: Item
instance of: scholarly article
title: The influence of \(\pi\)-quasinormality of some subgroups of a finite group.
zbMATH Open document ID: 1053.20017
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: A subgroup \(H\) of a finite group \(G\) is said to be \(\pi\)-quasinormal in \(G\) if it permutes with every Sylow subgroup of \(G\). Suppose that \(G\) is a group with a normal subgroup \(H\) such that all maximal subgroups of any Sylow subgroup of \(F^*(H)\) are \(\pi\)-quasinomal in \(G\). The main result in the paper states that if \(G/H\) is supersolvable then \(G\) is also supersolvable. The authors also obtain several applications of the above result to saturated formations containing the class of supersolvable groups.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 2051598
zbMATH Keywords: \(\pi\)-quasinormal subgroups
zbMATH Keywords: saturated formations
zbMATH Keywords: supersolvable groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: Sylow subgroups
author: Yangming Li
author: Yanming Wang
author: Huaquan Wei
reviewed by: Francisco Pérez-Monasor
MaRDI profile type: Publication
full work available at URL: s00013-003-0829-6
OpenAlex ID: W1968212654
DOI: 10.1007/S00013-003-0829-6
description: scientific article; zbMATH DE number 2051598