Bulletin of the
Korean Mathematical Society BKMS

A group $G$ is called cyclic subgroup separable for the cyclic subgroup $H$ if for each $x \in G \backslash H$, there exists a normal subgroup $N$ of finite index in $G$ such that $x \notin HN$. Clearly a cyclic subgroup separable group is residually finite. In this note we show that certain polygonal products of cyclic subgroup separable groups amalgamating normal subgroups are again cyclic subgroup separable. We then apply our results to polygonal products of polycyclic-by-finite groups and free-by-finite groups.

Keywords: subgroup separable, polygonal products, polycyclic-by-finite groups, free-by-finite groups, abelian groups

MSC numbers: Primary 20E06, 20E26, 20F18; Secondary 20F05