The structure of free groups of certain varieties

Let $F$ be a free group and $N\vartriangleleft F$. The structure of the group $G=F/[F,N']$ is studied. A description is obtained of the periodic part of $G$ in terms of the third and fourth homology groups of $B=F/N$. It is shown that, if $B$ is residually torsion-free nilpotent, the same is true for the factor group of $G$ by its periodic part.
Bibliography: 9 titles.