Freely decomposable automorphism groups
type: Item
instance of: scholarly article
title: Freely decomposable automorphism groups
zbMATH Open document ID: 0675.20031
DOI: 10.1007/BF01198347
author: Martin J. Evans
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: This article is a contribution to the question: which groups are automorphism groups? The following interesting theorem is proved. If G is a group such that Aut G is the free product H*K of non-trivial subgroups H and K, then \(| H| =2=| K|\). On the other hand if \(| H| =2=| K|\), then H*K is infinite dihedral, and hence is isomorphic with its automorphism group. The main tool in the proof is the Kurosh-Subgroup Theorem.
reviewed by: Derek J. S. Robinson
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 4105223
zbMATH Keywords: freely decomposable automorphism groups
zbMATH Keywords: free product
zbMATH Keywords: Kurosh-Subgroup Theorem
MaRDI profile type: Publication
cites work: Q5513066
cites work: INFINITE TORSION GROUPS AS AUTOMORPHISM GROUPS
description: scientific article; zbMATH DE number 4105223