Bounded automorphisms of groups
type: Item
instance of: scholarly article
title: Bounded automorphisms of groups
zbMATH Open document ID: 0816.20026
author: Renfang Jiang
published in: Journal of Algebra
publication date: 1994-09-28T00:00:00Z
review text: Let \(G\) be the fundamental group of a graph of groups (in the sense of Bass-Serre theory). Such a group has a natural length function and thus a corresponding notion of bounded subgroups and bounded automorphisms. The general result of this paper is that an automorphism of \(G\) is bounded if and only if it is induced by isomorphisms of vertex groups and inner automorphisms. In the special cases that \(G\) is an HNN-extension or an amalgamated free product \(G_ 1 *_{G_ 0} G_ 2\), more specific characterizations of bounded automorphisms are obtained. If moreover \(G_ 1\) and \(G_ 2\) are groups of type (FA), then a presentation of \(\text{Aut}(G)\) is given in terms of \(\text{Aut}(G_ i)\) \((i = 0,1,2)\). All proofs, most of which are rather elementary considerations in Bass- Serre theory, are given in full detail.
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 645114
zbMATH Keywords: fundamental group of a graph of groups
zbMATH Keywords: Bass-Serre theory
zbMATH Keywords: length function
zbMATH Keywords: bounded subgroups
zbMATH Keywords: bounded automorphisms
zbMATH Keywords: inner automorphisms
zbMATH Keywords: HNN-extension
zbMATH Keywords: amalgamated free product
zbMATH Keywords: presentation
reviewed by: Frank Herrlich
MaRDI profile type: Publication
full work available at URL: jabr.1994.1262
OpenAlex ID: W2015856673
DOI: 10.1006/JABR.1994.1262
description: scientific article; zbMATH DE number 645114