Conjugacy separability of generalized free products of surface groups Original Research Article

We prove that generalized free products of two free groups or finitely generated torsion-free nilpotent groups amalgamating a cyclic subgroup are cyclic conjugacy separable. Using this we prove that generalized free products of two surface groups amalgamating a cyclic subgroup are conjugacy separable. We conjecture that generalized free products of two Fuchsian groups amalgamating a cyclic subgroup are conjugacy separable.