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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Virtually splitting the map from $\operatorname {Aut}(G)$ to $\operatorname {Out}(G)$
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by Mathieu Carette PDF
Proc. Amer. Math. Soc. 143 (2015), 543-554 Request permission


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:
  • 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
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 543-554
  • MSC (2010): Primary 20F28; Secondary 20E36, 20F55, 20F67
  • DOI:
  • MathSciNet review: 3283643