4.69 (1973)

Let $G$ be a finite $p$-group, and suppose that $|G'| > p^{n(n-1)/2}$ for some non-negative integer $n$. Prove that $G$ is generated by the elements of breadths $\geqslant n$. The breadth of an element $x$ of $G$ is $b(x)$ where $|G : C_G(x)| = p^{b(x)}$.