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Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups
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- Journal:
- Canadian Mathematical Bulletin / Volume 42 / Issue 3 / 01 September 1999
- Published online by Cambridge University Press:
- 20 November 2018, pp. 335-343
- Print publication:
- 01 September 1999
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- Article
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We derive a necessary and sufficient condition for
$\text{HNN}$-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 $\text{HNN}$-extensions of abelian groups with cyclic associated subgroups. We also consider these residual properties of $\text{HNN}$-extensions of nilpotent groups with cyclic associated subgroups.
