  Let $G$ be a non-abelian finite simple group. A famous result of Liebeck and
Shalev is that there is an absolute constant $c$ such that whenever $S$ is a
non-trivial normal subset in $G$ then $S^{k} = G$ for any integer $k$ at least
$c \cdot (\log|G|/\log|S|)$. This result is generalized by showing that there
exists an absolute constant $c$ such that whenever $S_{1}, \ldots , S_{k}$ are
normal subsets in $G$ with $\prod_{i=1}^{k} |S_{i}| \geq {|G|}^{c}$ then $S_{1}
\cdots S_{k} = G$.
