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arXiv · 1111.3497

On the product decomposition conjecture for finite simple groups

Nick Gill·László Pyber·Ian Short·Endre Szabó
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Abstract

We prove that if $G$ is a finite simple group of Lie type and $S$ a subset of $G$ of size at least two then $G$ is a product of at most $c\log|G|/\log|S|$ conjugates of $S$, where $c$ depends only on the Lie rank of $G$. This confirms a conjecture of Liebeck, Nikolov and Shalev in the case of families of simple groups of Lie type of bounded rank.

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Nick Gill, László Pyber, Ian Short, Endre Szabó. 2011-11-15. On the product decomposition conjecture for finite simple groups. https://arxiv.org/abs/1111.3497

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