- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:00
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2013
4
On the product decomposition conjecture for finite simple groups
Nick
Gill
Open University, MILTON KEYNES, UNITED KINGDOM
László
Pyber
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Ian
Short
Open University, MILTON KEYNES, UNITED KINGDOM
Endre
Szabó
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
Conjugacy, Doubling Lemma, Product Theorem, simple group, width
We prove that if $G$ is a finite simple group of Lie type and $S$ is 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 bounded rank. We also obtain various related results about products of conjugates of a set within a group.
Group theory and generalizations
867
882
10.4171/GGD/208
http://www.ems-ph.org/doi/10.4171/GGD/208