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Normal automorphisms of relatively hyperbolic groups

By Ashot Minasyan and Denis Osin

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

Topics: QA
Year: 2010
OAI identifier: oai:eprints.soton.ac.uk:143193
Provided by: e-Prints Soton

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