Journal of the
Korean Mathematical Society JKMS

We give a characterization for fundamental groups of graphs of groups amalgamating cyclic edge subgroups to be cyclic subgroup separable if each pair of edge subgroups has a non-trivial intersection. We show that fundamental groups of graphs of abelian groups amalgamating cyclic edge subgroups are cyclic subgroup separable, hence residually finite, if each edge subgroup is isolated in its containing vertex group.

Keywords: residual finiteness, amalgamated free products, HNN extensions, tree products, fundamental groups of graphs of groups

MSC numbers: 20E26, 20E06, 20E08, 20F05