Geometry & Topology
- Geom. Topol.
- Volume 18, Number 5 (2014), 2985-3023.
Residual properties of automorphism groups of (relatively) hyperbolic groups
We show that is residually finite if is one-ended and hyperbolic relative to virtually polycyclic subgroups. More generally, if 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 is virtually residually –finite for every prime if is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually residually –finite.
Geom. Topol., Volume 18, Number 5 (2014), 2985-3023.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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