1. CMB 1999 (vol 42 pp. 335)
|Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups |
We derive a necessary and sufficient condition for HNN-extensions of cyclic subgroup separable groups with cyclic associated subgroups to be cyclic subgroup separable. Applying this, we explicitly characterize the residual finiteness and the cyclic subgroup separability of HNN-extensions of abelian groups with cyclic associated subgroups. We also consider these residual properties of HNN-extensions of nilpotent groups with cyclic associated subgroups.
Keywords:HNN-extension, nilpotent groups, cyclic subgroup separable $(\pi_c)$, residually finite
Categories:20E26, 20E06, 20F10