Conjugacy separability of certain 1-relator groups with torsion (Q1080950)

A group A is said to be conjugacy separable if for every pair of elements x, y in A which are not conjugate in A, there exists a finite homomorphic image \(\bar A\) of A such that the images of x, y in \(\bar A\) are not conjugate. In this paper it is proved that groups of the form \(<b,t\); \((t^{-1}b^{\ell}tb^ m)^ s>\), where \(s>1\) are conjugacy separable. Among the results used are the following. First a theorem of Dyer which states that the free product of two conjugacy separable groups with a finite amalgamated subgroup is conjugacy separable. Secondly, a theorem of Collins which states that an HNN extension of a conjugacy separable group in which a pair of finite isomorphic subgroups becomes conjugate is conjugacy separable. Finally a theorem of Tang, which states that \(<h,k\); \((h^ mk^{\ell})^ s>\) \((s>1)\) is conjugacy separable, is used. The context of the theorem and the known results about conjugacy separability are fully described in the introduction.