On the kernel of the Gassner representation

We study the Gassner representation of the pure braid group $P_n$ by considering its restriction to a free subgroup $F$. The kernel of the restriction is shown to lie in the subgroup $[{\mathrm{\Gamma }}^{3}F,{\mathrm{\Gamma }}^{2}F]$, sharpening a result of Lipschutz.