Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20F28, 20E36, 20F55, 20F67

Retrieve articles in all journals with MSC (2010): 20F28, 20E36, 20F55, 20F67


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

DOI: https://doi.org/10.1090/S0002-9939-2014-12278-7
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.