Subgroup separability, knot groups and graph manifolds

This paper answers a question of Burns, Karrass and Solitar by giving examp les of knot and link groups which are not subgroup-separable. For instance, it is shown that the fundamental group of the square knot complement is no t subgroup separable. Let L denote the fundamental group of the link consis ting of a chain of 4 circles. It is shown that L is not subgroup separable. Furthermore, it is shown that L is a subgroup of every known non-subgroup separable compact 3-manifold group. It is asked whether all such examples c ontain L.