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

TL;DR

This paper establishes conjugacy p-separability properties of right-angled Artin groups and explores their automorphism groups and related subgroups, with implications for residual finiteness and orderability.

Contribution

It proves conjugacy p-separability for subnormal subgroups of p-power index in right-angled Artin groups and applies this to automorphism groups and Torelli groups.

Findings

Subnormal subgroups of p-power index are conjugacy p-separable.

Right-angled Artin groups are conjugacy separable in torsion-free nilpotent groups.

Outer automorphism groups are virtually residually p-finite.

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 group is residually torsion-free nilpotent, hence residually p-finite and bi-orderable.