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

Emmanuel Toinet (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Domaines: Théorie des groupes [math.GR]

Emmanuel Toinet. Conjugacy p-separability of right-angled Artin groups and applications. 2013. ⟨hal-00519434v4⟩