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Commentarii Mathematici Helvetici

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Volume 91, Issue 4, 2016, pp. 609–627
DOI: 10.4171/CMH/397

Published online: 2016-10-24

Virtually compact special hyperbolic groups are conjugacy separable

Ashot Minasyan[1] and Pavel A. Zalesskiĭ[2]

(1) University of Southampton, United Kingdom
(2) Universidade de Brasília, Brazil

We prove that any word hyperbolic group which is virtually compact special (in the sense of Haglund and Wise) is conjugacy separable. As a consequence we deduce that all word hyperbolic Coxeter groups and many classical small cancellation groups are conjugacy separable. To get the main result we establish a new criterion for showing that elements of prime order are conjugacy distinguished. This criterion is of independent interest; its proof is based on a combination of discrete and profinite (co)homology theories.

Keywords: Conjugacy separable, virtually special groups, hyperbolic groups

Minasyan Ashot, Zalesskiĭ Pavel: Virtually compact special hyperbolic groups are conjugacy separable. Comment. Math. Helv. 91 (2016), 609-627. doi: 10.4171/CMH/397