Cyclic conjugacy separability and conjugacy separability of certain HNN extensions

Abstract

In this note, we give a criterion for certain HNN extensions of cyclic conjugacy separable (respectively conjugacy separable) groups with infinite cyclic associated subgroups to be again cyclic conjugacy separable (respectively conjugacy separable).

Communicated by Alexander Olshanskii

Keywords:

• Conjugacy separability
• cyclic conjugacy separability
• HNN extensions

MATHEMATICS SUBJECT CLASSIFICATION:

• 20E06
• 20E26
• 20F10

Acknowledgment

We would like to thank the anonymous referee for the constructive comments.