Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Normal automorphisms of relatively hyperbolic groups

Authors: A. Minasyan and D. Osin
Journal: Trans. Amer. Math. Soc. 362 (2010), 6079-6103
MSC (2010): Primary 20F65, 20F67, 20E26
Published electronically: June 16, 2010
MathSciNet review: 2661509
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An automorphism $ \alpha $ 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 show that for any such 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 finite non-trivial 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 infinitely many ends.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F65, 20F67, 20E26

Retrieve articles in all journals with MSC (2010): 20F65, 20F67, 20E26

Additional Information

A. Minasyan
Affiliation: School of Mathematics, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom.

D. Osin
Affiliation: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240

PII: S 0002-9947(2010)05067-6
Keywords: Relatively hyperbolic group, normal automorphism, outer automorphism group, group with infinitely many ends, residual finiteness, group-theoretic Dehn surgery.
Received by editor(s): September 30, 2008
Received by editor(s) in revised form: March 25, 2009, and March 31, 2009
Published electronically: June 16, 2010
Additional Notes: The first author was supported by the Swiss National Science Foundation grant PP002-116899.
The second author was supported by the NSF grant DMS-0605093 and by the RFBR grant 05-01-00895.
Dedicated: Dedicated to Professor A.L. Shmelkin on the occasion of his 70th birthday.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.