Growth in $\mathrm{SL}_3(ℤ/pℤ)$

Abstract

Let G = \mathrm{SL}_3 (ℤ/ p ℤ), 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| < |G|^{1-ε} for some ε > 0 . Then |A \cdot A \cdot A| > |A|^{1+δ} , where δ > 0 depends only on ε . We will also study subsets A ⊂ G that do not generate G . Other results on growth and generation follow.

Locations

• Journal of the European Mathematical Society - View - PDF