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ISSN 1088-6850(e) ISSN 0002-9947(p)

Normal automorphisms of relatively hyperbolic groups

Author(s): A. Minasyan; D. Osin
Journal: Trans. Amer. Math. Soc. 362 (2010), 6079-6103.
MSC (2010): Primary 20F65, 20F67, 20E26
Posted: June 16, 2010
MathSciNet review: 2661509
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Abstract: An automorphism $\alpha$ of a group is normal if it fixes every normal subgroup of setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we show that for any such group , has finite index in the subgroup of normal automorphisms. If, in addition, is non-elementary and has no finite non-trivial normal subgroups, then . As an application, we show that is residually finite for every finitely generated residually finite group with infinitely many ends.

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