  In this short note we confirm a conjecture of James Wiegold. We prove that if
$G$ is a finite $p$-group and $|G'|>p^{n(n-1)/2}$ for some non-negative integer
$n$, then the group $G$ can be generated by the elements of breadth at least
$n$. The breadth $b(x)$ of an element $x$ of a finite $p$-group $G$ is defined
by the equation $|G:C_G(x)| = p^{b(x)}$, where $C_G(x)$ is the centralizer of
$x$ in $G$.
