8.56 (1982)

Let $X$ be a finite set and $f$ a mapping from the set of subsets of $X$ to the positive integers. Under the requirement that in a group generated by $X$, every subgroup $\langle Y \rangle$, $Y \subseteq X$, be nilpotent of class $\leqslant f(Y)$, is it true that the free group $G_f$ relative to this condition is torsion-free?