An explicit upper bound for the Helfgott delta in SL(2,p)
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Helfgott proved that there exists a δ>0 such that if S is a symmetric generating subset of SL(2,p) containing 1 then either S3=SL(2,p) or |S3| ≥|S|1+δ. It is known that δ ≥ 1/3024. Here we show that δ ≤(log2(7)-1)/6 ≈ 0.3012 and we present evidence suggesting that this might be the true value of δ.
Button , J & Roney-Dougal , C 2015 , ' An explicit upper bound for the Helfgott delta in SL(2,p) ' , Journal of Algebra , vol. 421 , pp. 493-511 . https://doi.org/10.1016/j.jalgebra.2014.09.001
Journal of Algebra
Copyright © 2014 Published by Elsevier Inc. This is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra 421, 493-511, 1 January 2015 DOI https://doi.org/10.1016/j.jalgebra.2014.09.001