Geodesic
Solution of the generalized conjugacy problem for words in Coxeter groups of large type
Diskretnaya Matematika, Tome 17 (2005) no. 3, pp. 123-145.

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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. 
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V. N. Bezverkhnii; I. V. Dobrynina. Solution of the generalized conjugacy problem for words in Coxeter groups of large type. Diskretnaya Matematika, Tome 17 (2005) no. 3, pp. 123-145. http://geodesic.mathdoc.fr/item/DM_2005_17_3_a12/

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