## Geometry & Topology

### Residual properties of automorphism groups of (relatively) hyperbolic groups

#### 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.

#### Article information

Source
Geom. Topol., Volume 18, Number 5 (2014), 2985-3023.

Dates
Received: 10 June 2013
Revised: 5 February 2014
Accepted: 8 March 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732886

Digital Object Identifier
doi:10.2140/gt.2014.18.2985

Mathematical Reviews number (MathSciNet)
MR3285227

Zentralblatt MATH identifier
1338.20042

#### Citation

Levitt, Gilbert; Minasyan, Ashot. Residual properties of automorphism groups of (relatively) hyperbolic groups. Geom. Topol. 18 (2014), no. 5, 2985--3023. doi:10.2140/gt.2014.18.2985. https://projecteuclid.org/euclid.gt/1513732886

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