Conjugacy in normal subgroups of hyperbolic groups

Details Conjugacy in normal subgroups of hyperbolic groups Conjugacy in normal subgroups of hyperbolic groups

2009-06-08

arxiv.org/abs/0906.1606v2

Mathematics

Group Theory

Version 2: 17 pages; we now construct finitely presented examples as well; Introduction expanded and two new sections added at

Scientific paper

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.

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