Growth in SL3\mathrm{SL}_3(ℤ/ppℤ)

  • Harald Andrés Helfgott

    Georg-August-Universität Göttingen, Germany


Let G=SL3G = \mathrm{SL}_3(ℤ/ppℤ), pp 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| < |G|1-ε for some ε > 0. Then |A ∙ A ∙ A| > |A|1+δ, where δ > 0 depends only on ε.

Cite this article

Harald Andrés Helfgott, Growth in SL3\mathrm{SL}_3(ℤ/ppℤ). J. Eur. Math. Soc. 13 (2011), no. 3, pp. 761–851

DOI 10.4171/JEMS/267