2 00 6 On the profinite topology of right - angled Artin groups

In the present work, 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. Also, we show that right-angled Artin groups are conjugacy separable. Moreover, we investigate the profinite topology of F 2 × F 2 and of the group L in [22], which are the only obstructions for the subgroup separability of the right-angled Artin groups. We show that the profinite topology of the above groups is strongly connected with the profinite topology of F 2. Finally, we study the pronilpotent topology of right-angled Artin group and we retrieve the result of [7] that right-angled Artin groups are residually torsion-free nilpotent.