Separability properties of certain polygonal products of groups

Abstract

Let G=gfp{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 centralsubgroup separable groups, amalgamating trivial intersectingcentral subgroups, are double coset separable relative to certaincentral 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.