Mutually permutable products of finite groups. II
type: Item
instance of: scholarly article
title: Mutually permutable products of finite groups. II
zbMATH Open document ID: 0939.20018
published in: Journal of Algebra
publication date: 1999-12-20T00:00:00Z
review text: [For Part I see the authors and \textit{M. D. Pérez-Ramos}, ibid. 213, No. 1, 369-377 (1999; Zbl 0917.20020).] The finite group \(G=HK\) is the mutually permutable product of its subgroups \(H\) and \(K\) if \(H\) permutes with every subgroup of \(K\) and \(K\) permutes with every subgroup of \(H\). The following theorem is proved. Let \(\mathcal F\) be a saturated formation containing the class of supersoluble groups. If the commutator subgroup of \(G\) is nilpotent, then the \(\mathcal F\)-residual \(G^{\mathcal F}\) of the mutually permutable product \(G=HK\) can be written as \(G^{\mathcal F}=H^{\mathcal F}K^{\mathcal F}\). However, an easy example shows that an \(\mathcal F\)-projector of \(G\) in general cannot be obtained from the corresponding projectors of the factor subgroups.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 1348172
zbMATH Keywords: products of subgroups
zbMATH Keywords: factorized groups
zbMATH Keywords: saturated formations
zbMATH Keywords: mutually permutable subgroups
zbMATH Keywords: residuals
zbMATH Keywords: projectors
author: Adolfo Ballester-Bolinches
author: Mari Carmen Pedraza-Aguilera
reviewed by: Bernhard Amberg
MaRDI profile type: Publication
full work available at URL: jabr.1999.7858
OpenAlex ID: W4212764733
cites work: Q3134546
cites work: On finite products of totally permutable groups
cites work: Finite groups which are products of pairwise totally permutable subgroups
cites work: Mutually permutable products of finite groups
cites work: \(p\)-supersolvability of factorized finite groups
cites work: Finite soluble groups
cites work: The embedding of quasinormal subgroups in finite groups
DOI: 10.1006/JABR.1999.7858
description: scientific article; zbMATH DE number 1348172