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# Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups

Published:1999-09-01
Printed: Sep 1999
• Goansu Kim
• C. Y. Tang
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## Abstract

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
 MSC Classifications: 20E26 - Residual properties and generalizations; residually finite groups 20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 20F10 - Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70]