Residual properties of automorphism groups of (relatively) hyperbolic groups
Residual properties of automorphism groups of (relatively) hyperbolic groups
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 p-residually finite for every prime p if G is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually p-residually finite
2985-3023
Levitt, Gilbert
f2ea4e9a-a5a1-486d-ac04-53b4dde611f4
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
1 December 2014
Levitt, Gilbert
f2ea4e9a-a5a1-486d-ac04-53b4dde611f4
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Levitt, Gilbert and Minasyan, Ashot
(2014)
Residual properties of automorphism groups of (relatively) hyperbolic groups.
Geometry & Topology, 18 (5), .
(doi:10.2140/gt.2014.18.2985).
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 p-residually finite for every prime p if G is one-ended and toral relatively hyperbolic, or infinitely-ended and virtually p-residually finite
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Accepted/In Press date: 9 March 2014
e-pub ahead of print date: 1 December 2014
Published date: 1 December 2014
Organisations:
Pure Mathematics
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Local EPrints ID: 363212
URI: http://eprints.soton.ac.uk/id/eprint/363212
ISSN: 1465-3060
PURE UUID: 635abd9a-e2b2-408c-962c-6a8a7442aa82
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Date deposited: 21 Mar 2014 11:33
Last modified: 15 Mar 2024 03:29
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Author:
Gilbert Levitt
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