Conjugacy in normal subgroups of hyperbolic groups

Armando Martino; Ashot Minasyan

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arXiv · 0906.1606

Conjugacy in normal subgroups of hyperbolic groups

Armando Martino·Ashot Minasyan

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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.

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Armando Martino, Ashot Minasyan. 2009-06-08. Conjugacy in normal subgroups of hyperbolic groups. https://arxiv.org/abs/0906.1606

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