On Magnus groups

In this paper we consider groups of the form $F/V(N)$, where $V(N)$ is a verbal subgroup of a normal divisor $N$ of a group $F$, and $F$ is either free or the free product of certain groups. In the latter case we assume that $N$ is contained in the Cartesian subgroup. We prove that the factors of the lower central series of $F/V(N)$ are torsion-free or even free Abelian if the corresponding property is possessed by the factors of the lower central series of $F/N$ and $N/V(N)$.
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