Pure braid groups are not residually free

TL;DR

This paper proves that the Artin pure braid group on four or more strands is not residually free, and also determines its corank, providing new insights into its algebraic structure.

Contribution

It establishes that pure braid groups on at least four strands are not residually free and identifies the corank of pure braid groups on at least three strands.

Findings

Pure braid group on ≥4 strands is not residually free.

Pure braid group on ≥3 strands has corank two.

Provides new structural insights into pure braid groups.

Abstract

We show that the Artin pure braid group on at least four strands is not residually free. Our results also show that the pure braid group on at least three strands has corank two.