Automorphism groups of nilpotent groups
type: Item
instance of: scholarly article
title: Automorphism groups of nilpotent groups
zbMATH Open document ID: 1031.20032
author: Gábor Braun
author: Rüdiger Göbel
published in: Archiv der Mathematik
publication date: 2003-10-16T00:00:00Z
review text: \textit{M. Dugas} and \textit{R. Göbel} [Arch. Math. 54, No. 4, 340-351 (1990: Zbl 0703.20033)] proved the following result: if \(H\) is any group, there is a torsion-free nilpotent group \(G\) of class \(2\) such that \(\Aut(G)=H\ltimes\text{Stab}(G)\), where \(\text{Stab}(G)\) is the stability group of the series \(1\triangleleft Z(G)\triangleleft G\). This generalized a previous construction due to Zalesskij of a countably infinite torsion-free nilpotent group of class \(2\) with no outer automorphisms. In the present work the authors greatly extend the earlier theorem by showing that there is a full class of nilpotent groups of class \(2\) and infinite cardinality which have isomorphic automorphism groups with the same structure as in the earlier theorem.
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 1993478
zbMATH Keywords: torsion-free nilpotent groups
zbMATH Keywords: automorphism groups
reviewed by: Derek J. S. Robinson
MaRDI profile type: Publication
full work available at URL: s00013-003-0802-4
OpenAlex ID: W1990075847
DOI: 10.1007/S00013-003-0802-4
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description: scientific article; zbMATH DE number 1993478