#### Volume 18, issue 5 (2014)

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Residual properties of automorphism groups of (relatively) hyperbolic groups

### Gilbert Levitt and Ashot Minasyan

Geometry & Topology 18 (2014) 2985–3023
##### Abstract

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.

##### Keywords
relatively hyperbolic groups, outer automorphism groups, residually finite
##### Mathematical Subject Classification 2010
Primary: 20F67
Secondary: 20F28, 20E26
##### Publication
Received: 10 June 2013
Revised: 5 February 2014
Accepted: 8 March 2014
Published: 1 December 2014
Proposed: Martin R Bridson
Seconded: Walter Neumann, Cameron Gordon
##### Authors
 Gilbert Levitt Laboratoire de Mathématiques Nicolas Oresme Université de Caen et CNRS (UMR 6139) BP 5186 14032 CAEN Cedex 5 France Ashot Minasyan Mathematical Sciences University of Southampton Highfiled Southampton SO17 1BJ UK