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Proceedings of the American Mathematical Society

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Virtually splitting the map from $\operatorname {Aut}(G)$ to $\operatorname {Out}(G)$


Author: Mathieu Carette
Journal: Proc. Amer. Math. Soc. 143 (2015), 543-554
MSC (2010): Primary 20F28; Secondary 20E36, 20F55, 20F67
DOI: https://doi.org/10.1090/S0002-9939-2014-12278-7
Published electronically: October 10, 2014
MathSciNet review: 3283643
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Abstract: We give an elementary criterion on a group $G$ for the map $\operatorname {Aut}(G)$ $\to \operatorname {Out}(G)$ to split virtually. This criterion applies to many residually finite $\operatorname {CAT}(0)$ groups and hyperbolic groups, and in particular to all finitely generated Coxeter groups. As a consequence the outer automorphism group of any finitely generated Coxeter group is residually finite and virtually torsion-free.


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Additional Information

Mathieu Carette
Affiliation: Université catholique de Louvain, IRMP, Chemin du Cyclotron 2, bte L7.01.01, 1348 Louvain-la-Neuve, Belgium
Email: mathieu.carette@uclouvain.be

Keywords: Outer automorphism group, Coxeter group, residual finiteness
Received by editor(s): February 19, 2013
Received by editor(s) in revised form: May 23, 2013
Published electronically: October 10, 2014
Additional Notes: The author is a Postdoctoral Researcher of the F.R.S.-FNRS (Belgium).
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.