Counterexample to a question of A. Yu. Ol'shanskij (Q1174052)

At the Third All-Union Symposium on Group Theory, B. I. Plotkin posed the Question: Is it true that each locally nilpotent group is a homomorphic image of a torsion-free locally nilpotent group? In connection with this, A. Yu. Ol'shanskij posed the Question: Suppose \(X\) is a finite set and \(f\) is a function that assumes natural values on its subsets. We require that in a group with generating set \(X\) each subgroup \(\text{gr}(Y)\), \(Y\subseteq X\), be nilpotent of length at most \(f(Y)\). Is it true that a group that is free relative to this condition is torsion-free? An example is given which provides a negative answer to Ol'shanskij's question.