  It is known that the pure braid groups are residually torsion-free nilpotent.
This property is however widely open for the most obvious generalizations of
these groups, like pure Artin groups and like fundamental groups of hyperplane
complements (even reflection ones). In this paper we relate this problem to the
faithfulness of linear representations, and prove the residual torsion-free
nilpotence for a few other groups.
