Growth in SL_3(Z/pZ)

Abstract

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| < |G|^{1-ε} for some ε>0. Then |A\cdot A\cdot A|>|A|^{1+δ}, where δ>0 depends only on ε. We also study subsets A\subset G that do not generate G. Other results on growth and generation follow.

88 pages; Theorem 1.1 is new

References in corpus (3)

• A Strong Tits Alternative
• The sum-product phenomenon in arbitrary rings
• An explicit sum-product estimate in ${\mathbb{F}}_p$

Cited by in corpus (1)

• Approximate groups, II: the solvable linear case