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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.

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Published date: 2010
Organisations: Mathematics

Identifiers

Local EPrints ID: 143193
URI: https://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

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Date deposited: 08 Apr 2010 13:39
Last modified: 07 Aug 2019 00:39

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