On Generalised Free Products of Conjugacy Separable Groups Original Research Article

In this paper we prove that a free product of conjugacy separable groupsAandB, amalgamating a cyclic subgroup, is conjugacy separable ifAandBare subgroup separable, cyclic conjugacy separable, 2-free, and residuallyp-finite, for all prime numbersp. The following result is an example of the applications we obtain as consequences of our main theorem. LetAandBeach be a free product of surface groups, amalgamating a maximal cyclic subgroup. Then a free product ofAandB, amalgamating a cyclic subgroup, is conjugacy separable.