Conjugacy $p$-separability of right-angled Artin groups and applications

Abstract

We prove that every subnormal subgroup of $p$-power index in a right-angled Artin group is conjugacy $p$-separable. As an application, we prove that every right-angled Artin group is conjugacy separable in the class of torsion-free nilpotent groups. As another application, we prove that the outer automorphism group of a right-angled Artin group is virtually residually $p$-finite. We also prove that the Torelli group of a right-angled Artin group is residually torsion-free nilpotent, hence residually $p$-finite and bi-orderable.