Journal of the
Korean Mathematical Society JKMS

Let $G=(E*_A F)$, where $A$ is a finitely generated abelian subgroup. We prove a criterion for $G$ to be $\{A\}$-double coset separable. Applying this result, we show that polygonal products of central subgroup separable groups, amalgamating trivial intersecting central subgroups, are double coset separable relative to certain central subgroups of their vertex groups. Finally we show that such polygonal products are conjugacy separable. It follows that polygonal products of polycyclic-by-finite groups, amalgamating trivial intersecting central subgroups, are conjugacy separable.

Keywords: polygonal products, tree products, double coset separable, conjugacy separable, residually finite

MSC numbers: Primary 20E26, 20E06; Secondary 20F10