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Automorphisms of right-angled Artin groups

2012

The purpose of this thesis is to study the automorphisms of right-angled Artin groups. Given a finite simplicial graph $\Gamma$, the right-angled Artin group $G_\Gamma$ associated to $\Gamma$ is the group defined by the presentation whose generators are the vertices of $\Gamma$, and whose relators are commutators of pairs of adjacent vertices. The first chapter is intended as a general introduction to the theory of right-angled Artin groups and their automorphisms. In a second chapter, 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 th…