Residual properties of automorphism groups of (relatively) hyperbolic groups

Levitt, Gilbert¹ ; Minasyan, Ashot²

¹ Laboratoire de Mathématiques Nicolas Oresme, Université de Caen et CNRS (UMR 6139), BP 5186, 14032 CAEN Cedex 5, France
² Mathematical Sciences, University of Southampton, Highfiled Southampton SO17 1BJ, UK

Geometry & topology, Tome 18 (2014) no. 5, pp. 2985-3023.

Résumé

We show that $Out\left(G\right)$ is residually finite if $G$ is one-ended and hyperbolic relative to virtually polycyclic subgroups. More generally, if $G$ is one-ended and hyperbolic relative to proper residually finite subgroups, the group of outer automorphisms preserving the peripheral structure is residually finite. We also show that $Out\left(G\right)$ is virtually residually $p$–finite for every prime $p$ if $G$ is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually residually $p$–finite.

Détail

DOI : 10.2140/gt.2014.18.2985

Classification : 20F67, 20F28, 20E26
Keywords: relatively hyperbolic groups, outer automorphism groups, residually finite

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