Locally compact groups with permutable closed subgroups
type: Item
instance of: scholarly article
title: Locally compact groups with permutable closed subgroups
zbMATH Open document ID: 1506.22001
author: Karl H. Hofmann
author: Francesco Russo
author: Wolfgang Herfort
published in: Advances in Mathematics
publication date: 2021-09-23T00:00:00Z
review text: A totally disconnected topological group \(G\) is called \textit{periodic} if \(G\) has only compact elements. The authors of this paper intensively study the class of all periodic locally compact groups in their book [\textit{W. Herfort} et al., Periodic locally compact groups. Berlin etc.: de Gruyter (2019; Zbl 1423.22001)]. A locally compact group \(G\) is called \textit{strongly topologically quasihamiltonian} if \(G\) has permutable closed subgroups. (This means: For any two closed subgroups \(X\) and \(Y\) of \(G\) one has \(XY=YX\) and this product is closed.) In section 14 of their book [loc. cit.] the authors describe the class of those groups. Theorem 14.28 of that section is generalized by the main result (Theorem 1.2) of this interesting paper: A classification of all locally compact periodic strongly topologically quasihamiltonian groups is given.
reviewed by: Dieter Remus
Mathematics Subject Classification ID: 22A05
Mathematics Subject Classification ID: 22A26
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20K35
zbMATH DE Number: 7399492
zbMATH Keywords: quasihamiltonian groups
zbMATH Keywords: periodic locally compact groups
zbMATH Keywords: near abelian groups
MaRDI profile type: Publication
full work available at URL: j.aim.2021.107894
OpenAlex ID: W3186076083
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DOI: 10.1016/J.AIM.2021.107894
description: scientific article; zbMATH DE number 7399492