Growth in SL_3(Z/pZ)

By Harald Andrés Helfgott. 2008

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Let G=SL_3(Z/pZ), p a prime. Let A be a set of generators of G. Then A grows under the group operation. To be precise: denote by |S| the number of elements of a finite set S. Assume |A| 0. Then |A\cdot A\cdot A|>|A|^{1+\delta}, where \delta>0 depends only on \epsilon. We also study subsets A\subset G that do not generate G. Other results on growth and generation follow.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/91b95b25217d696b64b145f0c2be6b5814a2b61b