AN EXAMPLE OF A SUBGROUP SEPARABLE BUT NOT CONJUGACY SEPARABLE GROUP

We give an example of a conjugacy separable, but not subgroup separable group. It is an adaptation of an example of Tavgen and the third author from [Closed orbits and finite approximability with respect to conjugacy of free amalgamated products, Math. Notes58 (1995) 1042–1048] to a theorem of Raptis [On finiteness conditions of certain graphs of groups, Internat. J. Algebra Comput.5 (1995) 719–724].

Residual finiteness, subgroup separability and conjugacy separability of certain HNN extensions

In this note we shall give characterisations for HNN extensions of non-cyclic polycyclic-by-finite groups with normal infinite cyclic associated subgroups to be residually finite, subgroup separable and conjugacy separable.

THE FIGURE EIGHT KNOT GROUP IS CONJUGACY SEPARABLE

We prove that torsion free subgroups of GL2(ℂ) (abstractly) commensurable with the Euclidean Bianchi groups are conjugacy separable. As a consequence we deduce the result stated in the tittle.