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The automorphism group of accessible groups

par Carette, Mathieu
Référence Journal of the London Mathematical Society, 84, 3, page (731-748)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

In this article, we study the outer automorphism group of a group G decomposed as a finite graph of groups with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by taking extensions of relative automorphism groups of vertex groups, groups of Dehn twists and groups of automorphisms of free products. We apply this description and obtain a criterion for Out(G) to be finitely presented, as well as a necessary and sufficient condition for Out(G) to be finite. Consequences for hyperbolic groups are discussed. © 2011 London Mathematical Society.