Volume 18, issue 5 (2014)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts 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 $Out\left(G\right)$ 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