It is shown that certain torsion groups studied by Grigorchuk and by Gupta and Sidki are conjugacy separable. 1. Introduction. In [1, 2, 3], R. I. Grigorchuk introduced and studied some remarkable new examples of finitely generated torsion groups. These groups are residually finite and amenable, and they fall into 20 isomorphism classes of p-groups for each prime p. Grigorchuk solved a problem ...

In this paper we study conjugacy separability of subdirect products of two free (or hyperbolic) groups. We establish necessary and sufficient criteria and apply them to fibre products to produce a finitely presented group G1 in which all finite index subgroups are conjugacy separable, but which has an index 2 overgroup that is not conjugacy separable. Conversely, we construct a finitely present...