Some properties of free
groups of some soluble varieties of groups, J. London Math. Soc. (2)
63 (2001), 592-606.
Let F be a free group, and let \gamma_n(F) be the n-th term of
the lower central series of F. We prove that
F/[\gamma_j(F), \gamma_i(F), \gamma_k(F), \gamma_l(F)] are torsion
free and residually nilpotent for certain values of i,j,k and
i,j,k,l, respectively. In the process of proving this, we
prove that the analogous Lie rings are torsion free.