Mutually permutable products of finite groups
type: Item
instance of: scholarly article
title: Mutually permutable products of finite groups
zbMATH Open document ID: 0917.20020
published in: Journal of Algebra
publication date: 1999-05-31T00:00:00Z
full work available at URL: http://hdl.handle.net/10251/146182
review text: Let the finite group \(G=HK\) be the product of two subgroups \(H\) and \(K\) such that \(H\) permutes with every subgroup of \(K\) and \(K\) permutes with every subgroup of \(H\). It is shown that if \(K\) is nilpotent or if \(K\) is supersoluble and the commutator subgroup of \(G\) is nilpotent, then the supersoluble residuals of \(G\) and \(H\) coincide.
reviewed by: Bernhard Amberg
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 1270887
zbMATH Keywords: products of groups
zbMATH Keywords: factorized groups
zbMATH Keywords: supersoluble groups
zbMATH Keywords: nilpotent groups
zbMATH Keywords: soluble groups
zbMATH Keywords: supersoluble residuals
author: Adolfo Ballester-Bolinches
author: M. D. Pérez-Ramos
author: Mari Carmen Pedraza-Aguilera
MaRDI profile type: Publication
OpenAlex ID: W4212814771
cites work: On the supersolvability of finite groups
cites work: Classes of finite groups and their properties
cites work: On finite products of totally permutable groups
cites work: \(p\)-supersolvability of factorized finite groups
cites work: Finite soluble groups
cites work: Q3744347
cites work: The embedding of quasinormal subgroups in finite groups
DOI: 10.1006/JABR.1998.7653
description: scientific article; zbMATH DE number 1270887