Normal Automorphisms of Relatively Hyperbolic Groups
نویسنده
چکیده
An automorphism α 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 Autn(G) of normal automorphisms. If, in addition, G is non-elementary and has no non-trivial finite normal subgroups, then Autn(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.
منابع مشابه
Splittings and automorphisms of relatively hyperbolic groups
We study automorphisms of a relatively hyperbolic group G. When G is oneended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups of GLn(Z) fixing certain basis elements. When more general parabolic groups are allowed, these ...
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