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G^3, Special Session in Geometric Group Theory
January 10-13, 2001
part of the AMS/MAA joint meeting
New Orleans, LA, USA

Organizers
Phil Bowers, Martin Bridson, Stephen Brick, Jon Corson, Igor Mineyev

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A Class of Rigid Coxeter Groups
by
Anton Kaul
University of South Florida

A Coxeter Group W is said to be rigid if, given any two Coxeter systems (W, S) and (W, S'), there is an automorphism \rho:W --> W such that \rho(S) = S'. We consider the class of Coxeter systems (W, S) for which the Coxeter graph \GammaS is complete and has only odd edge labels (such a system is said to be of "type Kn"). It is shown that if W has a type Kn system, then any other system for W is also type Kn. Moreover the multiset of edge labels on \GammaS and \GammaS' agree. In particular, if all but one edge label of \GammaS are identical, then W is rigid.

Date received: September 18, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafm-02.