5.17 (1976)

If the finite group $G$ has the form $G = AB$ where $A$ and $B$ are nilpotent of classes $\alpha$ and $\beta$, respectively, then $G$ is soluble. Is $G^{(\alpha+\beta)} = 1$? One can ask the same question for infinite groups (or Lie algebras), but there is nothing known beyond Ito’s theorem: $A' = B' = 1$ implies $G^{(2)} = 1$.