18.12 (2014)

Let $G$ be a finitely generated group of intermediate growth. Is it true that there is a positive integer $m$ such that every element of the derived subgroup $G'$ is a product of at most $m$ commutators?

This assertion is valid for groups of polynomial growth, since they are almost nilpotent by Gromov’s theorem. On the other hand, there are groups of exponential growth (for example, free groups) for which this assertion is not true.