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- W199052398 abstract "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." @default.
- W199052398 created "2016-06-24" @default.
- W199052398 creator A5042641839 @default.
- W199052398 date "2012-05-11" @default.
- W199052398 modified "2023-09-23" @default.
- W199052398 title "Automorphisms of right-angled Artin groups" @default.
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