Geodesic
Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups
Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 335-343

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DOI

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.
DOI : 10.4153/CMB-1999-039-4
Mots-clés : 20E26, 20E06, 20F10, HNN-extension, nilpotent groups, cyclic subgroup separable (πc, residually finite 
Kim, Goansu; Tang, C. Y. Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups. Canadian mathematical bulletin, Tome 42 (1999) no. 3, pp. 335-343. doi: 10.4153/CMB-1999-039-4
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     author = {Kim, Goansu and Tang, C. Y.},
     title = {Cyclic {Subgroup} {Separability} of {HNN-Extensions} with {Cyclic} {Associated} {Subgroups}},
     journal = {Canadian mathematical bulletin},
     pages = {335--343},
     year = {1999},
     volume = {42},
     number = {3},
     doi = {10.4153/CMB-1999-039-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-039-4/}
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