Quasinormal subgroups of infinite groups.
type: Item
instance of: scholarly article
title: Quasinormal subgroups of infinite groups.
zbMATH Open document ID: 1317.20033
author: Antonella Leone
published in: Ricerche di Matematica
publication date: 2014-12-08T00:00:00Z
review text: It is well-known that if \(G\) is a finite group and \(H\) is a quasinormal subgroup of \(G\), that is, \(H\) satisfies \(HK=KH\) for every \(K\leq G\), then \(H\) is subnormal in \(G\), \(H/H_G\) is nilpotent, and it even is contained in the hypercentre of \(G/H_G\). It is also well-known that none of these three assertions is true for arbitrary groups. The author gives a survey (without proofs) of what is known to hold under suitable assumptions on \(G\) or \(H\).
reviewed by: Roland Schmidt
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 6378245
zbMATH Keywords: quasinormal subgroups
zbMATH Keywords: permutable subgroups
zbMATH Keywords: infinite groups
MaRDI profile type: Publication
full work available at URL: s11587-014-0195-7
OpenAlex ID: W2013496493
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DOI: 10.1007/S11587-014-0195-7
description: scientific article; zbMATH DE number 6378245