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A generalization of the diameter bound of Liebeck and Shalev for finite simple groups (2003.14270v2)
Published 31 Mar 2020 in math.GR
Abstract: 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 $S_{1} \cdots S_{k} = G$.