Infinite groups with Sylow permutable subgroups.
type: Item
instance of: scholarly article
title: Infinite groups with Sylow permutable subgroups.
zbMATH Open document ID: 1213.20025
author: L. A. Kurdachenko
author: Tatiana Pedraza
author: Adolfo Ballester-Bolinches
author: Javier Otal
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2010-10-26T00:00:00Z
review text: Let \(G\) be a periodic group. A subgroup \(H\) of \(G\) is said to be `\(S\)-permutable' if \(HP=PH\) for each Sylow subgroup \(P\) of \(G\). It is known that \(S\)-permutability is not a transitive relation, and a `PST-group' is a periodic group in which \(S\)-permutability is transitive. In the paper under review, the authors extend a result of \textit{R. K. Agrawal} [Proc. Am. Math. Soc. 47, 77-83 (1975; Zbl 0299.20014)] on finite PST-groups to the case of radical hyperfinite groups (recall here that a group is `hyperfinite' if it has an ascending normal series with finite factors). Moreover, the relationship between PST-groups and groups in which all ascendant subgroups are \(S\)-permutable is investigated.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 5805948
zbMATH Keywords: periodic groups
zbMATH Keywords: ascendant subgroups
zbMATH Keywords: hyperfinite groups
zbMATH Keywords: permutable subgroups
zbMATH Keywords: transitive permutability
zbMATH Keywords: Sylow subgroups
MaRDI profile type: Publication
full work available at URL: s10231-009-0123-8
OpenAlex ID: W2090677994
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DOI: 10.1007/S10231-009-0123-8
description: scientific article; zbMATH DE number 5805948