The conjugacy separability of certain HNN extensions with cyclic associated subgroups

P.C.WONG  AND  C.K. TANG

Research Report No. 13/2001

Abstract

A group $G$ is said to be conjugacy separable if for each pair of elements $x,y\in G$ such that $x$ and $y$ are not conjugate in $G$, there exists a finite homomorphic image $\bar G$ of $G$ such that the images of $x$ and $y$ are not conjugate in $\bar G$. In this note, we show that certain HNN extensions and generalised free products are conjugacy separable.