Rapid growth in finite simple groups
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- by Martin W. Liebeck, Gili Schul and Aner Shalev PDF
- Trans. Amer. Math. Soc. 369 (2017), 8765-8779 Request permission
Abstract:
We show that small normal subsets $A$ of finite simple groups grow very rapidly; namely, $|A^2| \ge |A|^{2-\epsilon }$, where $\epsilon >0$ is arbitrarily small. Extensions, consequences, and a rapid growth result for simple algebraic groups are also given.References
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Additional Information
- Martin W. Liebeck
- Affiliation: Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
- MR Author ID: 113845
- ORCID: 0000-0002-3284-9899
- Gili Schul
- Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
- MR Author ID: 930758
- Aner Shalev
- Affiliation: Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel
- MR Author ID: 228986
- ORCID: 0000-0001-9428-2958
- 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. - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 8765-8779
- MSC (2010): Primary 20D06, 20F69
- DOI: https://doi.org/10.1090/tran/6935
- MathSciNet review: 3710643