On the product decomposition conjecture for finite simple groups

Details On the product decomposition conjecture for finite simple groups On the product decomposition conjecture for finite simple groups

2011-11-15

arxiv.org/abs/1111.3497v1

Mathematics

Group Theory

8 pages

Scientific paper

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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