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Rapid growth in finite simple groups


Authors: Martin W. Liebeck, Gili Schul and Aner Shalev
Journal: Trans. Amer. Math. Soc. 369 (2017), 8765-8779
MSC (2010): Primary 20D06, 20F69
DOI: https://doi.org/10.1090/tran/6935
Published electronically: June 13, 2017
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Abstract: We show that small normal subsets $ A$ of finite simple groups grow very rapidly; namely, $ \vert A^2\vert \ge \vert A\vert^{2-\epsilon }$, where $ \epsilon >0$ is arbitrarily small. Extensions, consequences, and a rapid growth result for simple algebraic groups are also given.


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Additional Information

Martin W. Liebeck
Affiliation: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom

Gili Schul
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

Aner Shalev
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

DOI: https://doi.org/10.1090/tran/6935
Received by editor(s): April 20, 2015
Received by editor(s) in revised form: October 13, 2015, and March 3, 2016
Published electronically: June 13, 2017
Additional Notes: The first and third authors acknowledge the support of EPSRC Mathematics Platform grant EP/I019111/1
The second and third authors acknowledge the support of an ERC advanced grant 247034 and of an Israel Science Foundation grant 1117/13
The third author acknowledges the support of the Vinik Chair of Mathematics, which he holds.
Article copyright: © Copyright 2017 American Mathematical Society

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