Verbal products of Magnus groups

A Magnus group is a group in which the intersection of the lower central series is trivial and its factors are torsion free.
The main result of the paper is the following theorem.
Theorem. If $\mathfrak B$ is the variety of all nilpotent groups of a certain class or the variety of all metabelian groups, or their intersection, and if free groups of $\mathfrak B$ and of $\mathfrak U\mathfrak B$ are Magnus groups, then the $\mathfrak U\mathfrak B$-product of any Magnus $\mathfrak B$-groups is a Magnus group.
Bibliography: 18 titles.