Finding representatives for the orbits under the automorphism group of a bounded Abelian group
type: Item
instance of: scholarly article
title: Finding representatives for the orbits under the automorphism group of a bounded Abelian group
zbMATH Open document ID: 0916.20040
author: Martin Schwachhöfer
author: Markus Stroppel
published in: Journal of Algebra
publication date: 1999-05-25T00:00:00Z
review text: The authors determine representatives of the orbits of a bounded abelian \(p\)-group under its automorphism group, and count the orbits. Their survey of the literature is cursory, which is unfortunate since the problem was solved 45 years ago by \textit{I. Kaplansky} [Infinite Abelian Groups, University of Michigan Press (1954; Zbl 0057.01901), Chapter 18].
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K10
zbMATH DE Number: 1251302
zbMATH Keywords: bounded Abelian \(p\)-groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: numbers of orbits
reviewed by: Phillip Schultz
MaRDI profile type: Publication
full work available at URL: jabr.1998.7623
OpenAlex ID: W1978805845
cites work: The Automorphisms of Countable Primary Reduced Abelian Groups†
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cites work: Q3270637
cites work: Q3281123
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cites work: Zur Theorie der überabzählbaren abelschen \(p\)-Gruppen
cites work: Eine Charakterisierung gewisser abelscher \(p\)-Gruppen
cites work: Q5339345
cites work: Groups that are almost homogeneous
DOI: 10.1006/JABR.1998.7623
description: scientific article; zbMATH DE number 1251302