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 residually torsion-free nilpotent. Moreover, we investigate the profinite topology of F2 × F2 and of the group L in [18], 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 F2.