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

Abstract

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.