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

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

2010-09-20

arxiv.org/abs/1009.3859v3

Mathematics

Group Theory

Scientific paper

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.

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