An explicit upper bound for the Helfgott delta in SL(2,p)

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Button, Jack; Roney-Dougal, Colva M;
  • Publisher: Journal of Algebra
  • Related identifiers: doi: 10.1016/j.jalgebra.2014.09.001
  • Subject: QA | Simple group | Subset growth | Mathematics - Combinatorics | QA Mathematics | Approximate subgroup | Mathematics - Group Theory | T-NDAS

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 S^3=SL(2, p)or |S^3| ≥|S|^1+ δ. It is known that δ ≥ 1/3024. Here we show that δ ≤ (log_2 (7) −1)/6 ≈ 0.3012and we present evidence suggesting t... View more
  • References (9)

    [1] L. Babai, N. Nikolov and L. Pyber, Product growth and mixing in finite groups, in: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, 2008, 248-257.

    [2] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24 (1997), 235-265.

    [3] J. Bourgain and A. Gamburd, Uniform expansion bounds for Cayley graphs of SL2(Fp), Ann. of Math. 167 (2008), 625-642.

    [4] E. Breuillard, B. Green and T. Tao, Approximate subgroups of linear groups, Geom. Funct. Anal. 21 (2011), 774-819.

    [5] H. A. Helfgott, Growth and generation in SL2(Z/pZ), Ann. of Math. 167 (2008), 601-623.

    [6] Huppert, B. Endliche Gruppen I. Grundlehren Math. Wiss. 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967

    [7] E. Kowalski, Explicit growth and expansion for SL2, Int. Math. Res. Notices 2013 (2013), 5645-5708.

    [8] W. Ledermann, Introduction to group theory, Longman, 1973.

    [9] L. Pyber and E. Szabo´, Growth in finite simple groups of Lie type of bounded rank, (2010).

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