14.16 (1999)

Following Yu. I. Merzlyakov we define the width of a verbal subgroup $V(G)$ of a group $G$ with respect to the set of words $V$ as the smallest $m \in \mathbb{N} \cup \{\infty\}$ such that every element of $V(G)$ can be written as a product of $\leqslant m$ values of words from $V \cup V^{-1}$. It is known that the width of any verbal subgroup of a finitely generated group of polynomial growth is finite. Is this statement true for finitely generated groups of intermediate growth?