SCHWEITZER 1981 Problem 4

Let $G$ be finite group and $\mathcal{K}$ a conjugacy class of $G$ that generates $G$ . Prove that the following two statements are equivalent:

(1) There exists a positive integer $m$ such that every element of $G$ can be written as a product of $m$ (not necessarily distinct) elements of $\mathcal{K}$ .

(2) $G$ is equal to its own commutator subgroup.

J. Denes