Conjugacy in normal subgroups of hyperbolic groups
Conjugacy in normal subgroups of hyperbolic groups
Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N. We show that the hyperbolic group from F. Haglund's and D. Wise's version of Rips's construction is hereditarily conjugacy separable. We then use this construction to produce first examples of finitely generated and finitely presented conjugacy separable groups that contain non-(conjugacy separable) subgroups of finite index.
Hereditary conjugacy separability, normal subgroups of hyperbolic groups, Rips's construction
889-909
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
September 2012
Martino, Armando
65f1ff81-7659-4543-8ee2-0a109be286f1
Minasyan, Ashot
3de640f5-d07b-461f-b130-5b1270bfdb3d
Martino, Armando and Minasyan, Ashot
(2012)
Conjugacy in normal subgroups of hyperbolic groups.
Forum Mathematicum, 24 (5), .
(doi:10.1515/FORM.2011.089).
Abstract
Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N. We show that the hyperbolic group from F. Haglund's and D. Wise's version of Rips's construction is hereditarily conjugacy separable. We then use this construction to produce first examples of finitely generated and finitely presented conjugacy separable groups that contain non-(conjugacy separable) subgroups of finite index.
Text
hcs_rips-h.pdf
- Author's Original
More information
Accepted/In Press date: 1 December 2010
Published date: September 2012
Keywords:
Hereditary conjugacy separability, normal subgroups of hyperbolic groups, Rips's construction
Organisations:
Pure Mathematics
Identifiers
Local EPrints ID: 142319
URI: http://eprints.soton.ac.uk/id/eprint/142319
ISSN: 0933-7741
PURE UUID: 3b851574-cf0d-40b7-801d-cba735e4738b
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Date deposited: 08 Apr 2010 13:47
Last modified: 14 Mar 2024 02:54
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