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Groups, Geometry, and Dynamics


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Volume 7, Issue 3, 2013, pp. 751–790
DOI: 10.4171/GGD/205

Published online: 2013-08-27

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

Emmanuel Toinet[1]

(1) Université de Bourgogne, Dijon, France

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.

Keywords: Right-angled Artin group, automorphism group, Torelli group, residual properties, separability properties, pro-$p$ topology

Toinet Emmanuel: Conjugacy $p$-separability of right-angled Artin groups and applications. Groups Geom. Dyn. 7 (2013), 751-790. doi: 10.4171/GGD/205