On the residual solvability of generalized free products of solvable groups

In this paper, we study the residual solvability of the generalized free product of solvable groups.Comment: Discrete Mathematics & Theoretical Computer Science, Vol 13, 201

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.Comment: Version 3: 18 pages; corrected a problem with justification of Corollary 8.