1 March 2001 Finite linear groups and bounded generation
Martin W. Liebeck, L. Pyber
Duke Math. J. 107(1): 159-171 (1 March 2001). DOI: 10.1215/S0012-7094-01-10718-7


We extend a result of E. Hrushovski and A. Pillay as follows. Let G be a finite subgroup of GL(n,$\mathbb{F}$) where $\mathbb{F}$ is a field of characteristic p such that p is sufficiently large compared to n. Assume that G is generated by p-elements. Then G is a product of 25 of its Sylow p-subgroups.

If G is a simple group of Lie type in characteristic p, the analogous result holds without any restriction on the Lie rank of G.

We also give an application of the Hrushovski-Pillay result showing that finitely generated adelic profinite groups are boundedly generated (i.e., such a group is a product of finitely many closed procyclic subgroups). This confirms a conjecture of V. Platonov and B. Sury which was motivated by characterizations of the congruence subgroup property for arithmetic groups.


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Martin W. Liebeck. L. Pyber. "Finite linear groups and bounded generation." Duke Math. J. 107 (1) 159 - 171, 1 March 2001. https://doi.org/10.1215/S0012-7094-01-10718-7


Published: 1 March 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1017.20039
MathSciNet: MR1815254
Digital Object Identifier: 10.1215/S0012-7094-01-10718-7

Primary: 20G40
Secondary: 20E18

Rights: Copyright © 2001 Duke University Press


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Vol.107 • No. 1 • 1 March 2001
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