Tree products of conjugacy separable groups

A group G is said to be conjugacy separable if for each pair of elements x, y is an element of G such that x and y are not conjugate in G, there exist s a finite homomorphic image (G) over bar of G such that the images of x, y are not conjugate in (G) over bar. In this note, we show that the tree pro ducts of finitely many conjugacy separable and subgroup separable groups am algamating central subgroups with trivial intersections are conjugacy separ able. We then apply our results to polycyclic-by-finite groups and free-by- finite groups. (C) 1999 Academic Press.