Homogeneous locally compact groups
type: Item
instance of: scholarly article
title: Homogeneous locally compact groups
zbMATH Open document ID: 0889.22005
published in: Journal of Algebra
publication date: 1998-02-11T00:00:00Z
review text: Motivated by their occurrence in topological geometry, the author studies locally compact groups that are homogeneous in the sense that their automorphism group acts transitively on the non-identity elements. The main results say that compact homogeneous groups are precisely the arbitrary powers of cyclic groups of prime order (with product topology), that connected, locally compact, homogeneous groups are precisely the (additive groups of) vector spaces of finite dimension over the real numbers, and that abelian, locally compact, homogeneous groups are precisely the following: (1) the vector spaces of finite dimension over a nondiscrete locally compact field, (2) the divisible hulls of arbitrary powers of the group of \(p\)-adic integers, (3) all discrete vector spaces over a prime field (finite or the rationals), (4) the compact groups already mentioned, (5) the direct products of a group of type (3) and a group of type (4), based on the same prime number. -- Among the homogeneous, locally compact abelian groups, those of type (1) are characterized by being of countable weight and neither compact nor discrete.
Mathematics Subject Classification ID: 22B05
Mathematics Subject Classification ID: 22D05
zbMATH DE Number: 1117780
zbMATH Keywords: locally compact groups
zbMATH Keywords: compact homogeneous groups
author: Markus Stroppel
reviewed by: Rainer Löwen
MaRDI profile type: Publication
full work available at URL: jabr.1997.7202
OpenAlex ID: W2008334149
cites work: Q5580319
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cites work: On some types of topological groups
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DOI: 10.1006/JABR.1997.7202
description: scientific article; zbMATH DE number 1117780