On the profinite topology of right-angled Artin groups

We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups. We show that the profinite topology of the above group is strongly connected with the profinite topology of the free group of rank two.Comment: The previous version had an incomplete proof that right-angled Artin groups are conjugacy separable. A much more general result is proved by Minasyan in arXiv:0905.128

On the residual finiteness of outer automorphisms of relatively hyperbolic groups

We show that every virtually torsion-free subgroup of the outer automorphism group of a conjugacy separable relatively hyperbolic group is residually finite. As a direct consequence, we obtain that the outer automorphism group of a limit group is residually finite.Comment: 11 pages, 1 figure. Section 3 is replaced by Theorem 1.3. More detailed arguments. Added new references. To appear in Journal of Pure and Applied Algebr