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 subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. In particular, every right-angled Artin group is conjugacy p-separable. A consequence of this result is that the outer automorphism group of a right-angled Artin group is virtually residually p-finite. Another consequence of this result is that the outer automorphism group of a right-angled Artin group is K-residual, where K is the class of all outer automorphism groups of finite p-groups. 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. 2010. ⟨hal-00519434v3⟩