International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 976390, 10 pages
doi:10.1155/2008/976390
Research Article
Automorphisms of Right-Angled Coxeter Groups
1Department of Mathematics, Tufts University, Medford, MA 02155, USA
2Mathematics Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA
Received 16 May 2008; Accepted 12 August 2008
Academic Editor: Alexander Rosa
Copyright © 2008 Mauricio Gutierrez and Anton Kaul. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
If (W,S) is a right-angled Coxeter system, then Aut(W) is a semidirect product of the group Aut∘(W) of symmetric automorphisms by the automorphism group of a certain groupoid. We show that, under mild conditions, Aut∘(W) is a semidirect product of Inn(W) by the quotient Out∘(W)=Aut∘(W)/Inn(W). We also give sufficient conditions for the compatibility of the two semidirect products. When this occurs there is an induced splitting of the sequence 1→Inn(W)→Aut(W)→Out(W)→1 and consequently, all group extensions 1→W→G→Q→1 are trivial.