A characterization of totally disconnected compactly ruled groups
type: Item
instance of: scholarly article
title: A characterization of totally disconnected compactly ruled groups
zbMATH Open document ID: 1490.22006
author: Hatem Hamrouni
author: Zouhour Jlali
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2021-05-04T00:00:00Z
review text: A locally compact group \(G\) is \emph{compactly ruled} if it is a directed union of compact open subgroups. The class of compactly ruled groups is a proper subclass of the class of all compactly covered groups. Here it is shown that \(G\) is totally disconnected and compactly ruled iff the set of all compact open subgroups is dense in \(\mathrm{SUB}(G)\), where \(\mathrm{SUB}(G)\) denotes the Chabauty space of closed subgroups of \(G\). This is a natural extension of Gartside-Smith result for profinite groups. It is worth to highlight that the argument is based on the notion of a \emph{periodic element}, i.e., an element which generates a relatively compact subgroup. Notice that in literature such an element is also known as \emph{compact element}.
reviewed by: I. Castellano
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 7343571
zbMATH Keywords: locally compact group
zbMATH Keywords: compactly ruled
zbMATH Keywords: totally disconnected
zbMATH Keywords: compact open
zbMATH Keywords: periodic
MaRDI profile type: Publication
full work available at URL: s12044-020-00601-8
OpenAlex ID: W3165296499
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DOI: 10.1007/S12044-020-00601-8
description: scientific article; zbMATH DE number 7343571