Conjugacy separability of HNN-extensions of abelian groups (Q2365003)

We consider the conjugacy separability of HNN-extensions of abelian groups with cyclic associated subgroups. We show that if either the associated subgroups intersect trivially or the associated subgroups have a common subgroup of the same index then the HNN-extensions are conjugacy separable. Applying this result we completely characterize the conjugacy separability of HNN-extensions of abelian groups with cyclic associated subgroups.