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Cyclic Subgroup Separability of HNN-Extensions with Cyclic Associated Subgroups

Published online by Cambridge University Press:  20 November 2018

Goansu Kim  and
C. Y. Tang
Goansu Kim
Affiliation:
Department of Mathematics Yeungnam University Kyongsan, 712-749 Korea, email: gskim@ynucc.yeungnam.ac.kr
C. Y. Tang
Affiliation:
University of Waterloo Waterloo, Ontario N2L 3G1, email: fcytang@math.uwaterloo.ca
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Abstract

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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.

Keywords

20E2620E0620F10HNN-extensionnilpotent groupscyclic subgroup separable (πcresidually finite
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 335 - 343
Copyright
Copyright © Canadian Mathematical Society 1999

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