A Criterion for the Conjugacy Separability of Amalgamated Free Products of Conjugacy Separable Groups

Abstract

We first prove a criterion for the conjugacy separability of generalized free products of two conjugacy separable groups amalgamating a cyclic subgroup. Applying this result, we show that tree products of a finite number of conjugacy separable, residually finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups are conjugacy separable. From this we derive that tree products of finitely generated torsion-free nilpotent groups, free groups, or surface groups amalgamating cyclic subgroups are conjugacy separable.