Geometry & Topology

Residual properties of automorphism groups of (relatively) hyperbolic groups

Gilbert Levitt and Ashot Minasyan

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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

Subjects
Primary: 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 20F28: Automorphism groups of groups [See also 20E36] 20E26: Residual properties and generalizations; residually finite groups

Keywords
relatively hyperbolic groups outer automorphism groups residually finite

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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