Communications of the
Korean Mathematical Society CKMS

We first prove a criterion for the conjugacy separability of free products with amalgamation where the amalgamated subgroup is not necessarily cyclic. Applying this result, we show that free products of finite number of polycyclic-by-finite groups with central amalgamation are conjugacy separable. We also show that polygonal products of polycyclic-by-finite groups, amalgamating central cyclic subgroups with trivial intersections, are conjugacy separable.

Keywords: generalized free products, polygonal products, conjugacy separable, residually finite, polycyclic-by-finite groups

MSC numbers: 20E26, 20E06, 20F10