Hereditary conjugacy separability of right-angled Artin groups and its applications

Minasyan, Ashot

doi:10.4171/GGD/160

Groups, Geometry, and Dynamics

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GGD summary

Volume 6, Issue 2, 2012, pp. 335–388

DOI: 10.4171/GGD/160

Hereditary conjugacy separability of right-angled Artin groups and its applications

Ashot Minasyan (1)

(1) School of Mathematics, University of Southampton, Highfield, SO17 1BJ, SOUTHAMPTON, UNITED KINGDOM

We prove that finite-index subgroups of right-angled Artin groups are conjugacy separable. We then apply this result to establish various properties of other classes of groups. In particular, we show that any word hyperbolic Coxeter group contains a conjugacy separable subgroup of finite index and has a residually finite outer automorphism group. Another consequence of the main result is that Bestvina–Brady groups are conjugacy separable and have solvable conjugacy problem.

Keywords: Hereditary conjugacy separability, right-angled Artin groups, graph groups, partially commutative groups, Coxeter groups, Bestvina–Brady groups