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Combinatorial and Geometric Group Theory
May 5-10, 2006
Vanderbilt University
Nashville, TN, USA

Organizers
Goulnara Arzhantseva, Mike Mihalik, Denis Osin, Mark Sapir, Efim Zelmanov

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Orthogonal systems in graphs and free partially commutative groups
by
Ilya Kazachkov
McGill University
Coauthors: Andrew Duncan, Vladimir Remeslennikov

Let G be a finite graph and GG be the corresponding free partially commutative group. We construct orthogonality theory for graphs and free partially commutative groups and then use it to construct a nice theory of parabolic and quasiparabolic subgroups.

As applications we obtain a description of the centraliser of an arbitrary subset of GG and compute the height of the lattice of centralisers of GG.

Date received: March 30, 2006

Copyright © 2006 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 # casy-02.