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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(G) 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(G) 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
References
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