Residual nilpotence for generalizations of pure braid groups

TL;DR

This paper investigates the residual torsion-free nilpotence property in generalized pure braid groups, linking it to linear representation faithfulness and establishing this property for several new classes of groups.

Contribution

It connects residual torsion-free nilpotence to linear representation faithfulness and proves this property for certain generalized pure braid groups.

Findings

Residual torsion-free nilpotence established for some generalized groups

Links between linear representations and group properties clarified

Extends known properties from pure braid groups to new classes

Abstract

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.