Solution of the generalized conjugacy problem for words in Coxeter groups of large type

For a Coxeter group of large type, we give a solution of the generalised conjugacy problem for words: it is proved that the centraliser of a finitely generated subgroup is finitely generated and there exists an algorithm which yields its generators. It is shown that in the general case the centraliser of a finitely generated group is not cyclic. We construct an example of a group of this class which is not a hyperbolic group.
This research was supported by the Ministry of Education of the Russian Federation, grant 02–1.1–209.