Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups

摘要

We derive a necessary and sufficient condition for HNN-extensionsof cyclic subgroup separable groups with cyclic associatedsubgroups to be cyclic subgroup separable. Applying this, weexplicitly characterize the residual finiteness and the cyclicsubgroup separability of HNN-extensions of abelian groups withcyclic associated subgroups. We also consider these residualproperties of HNN-extensions of nilpotent groups with cyclicassociated subgroups.