Conjugacy Separability of Certain HNN Extensions of Conjugacy-Separable Groups

A group G is said to be conjugacy-separable if, for each pair of elements x, y G such that x and y are not conjugate in G, there exists a finite homomorphic image G¯ of G such that the images of x and y are not conjugate in G¯. In this paper, we show that certain HNN extensions of conjugacy-separable groups are conjugacy-separable. We then apply our results to HNN extensions of polycyclic-by-finite groups.2000 Mathematics Subject Classification: primary 20E26, 20E06; secondary 20F05