The University of Southampton
University of Southampton Institutional Repository

Normal automorphisms of relatively hyperbolic groups

Normal automorphisms of relatively hyperbolic groups
Normal automorphisms of relatively hyperbolic groups
An automorphism of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Aut_n(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal subgroups, then Aut_n(G)=Inn(G). As an application, we show that Out(G) is residually finite for every finitely generated residually finite group G with more than one end.
0002-9947
6079-6103
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Osin, Denis
32a9932c-f439-4b83-b639-1a53ac6bf6f5

Minasyan, Ashot and Osin, Denis (2010) Normal automorphisms of relatively hyperbolic groups. Transactions of the American Mathematical Society, 362, 6079-6103. (doi:10.1090/S0002-9947-2010-05067-6).

Record type: Article

Abstract

An automorphism of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Aut_n(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal subgroups, then Aut_n(G)=Inn(G). As an application, we show that Out(G) is residually finite for every finitely generated residually finite group G with more than one end.

Text
norm-aut-33.pdf - Author's Original
Download (371kB)

More information

Published date: 2010
Organisations: Mathematics

Identifiers

Local EPrints ID: 143193
URI: http://eprints.soton.ac.uk/id/eprint/143193
ISSN: 0002-9947
PURE UUID: 6db66a6a-3728-4e64-805c-46ce0e65b72f
ORCID for Ashot Minasyan: ORCID iD orcid.org/0000-0002-4986-2352

Catalogue record

Date deposited: 08 Apr 2010 13:39
Last modified: 14 Mar 2024 02:53

Export record

Altmetrics

Contributors

Author: Ashot Minasyan ORCID iD
Author: Denis Osin

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×