#### 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