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RESEARCH PRODUCT

Automorphisms of right-angled Artin groups

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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 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. In a third chapter, we give a presentation of the subgroup $Conj(G_\Gamma)$ of $Aut(G_\Gamma)$ consisting of the automorphisms that send each generator to a conjugate of itself.