Growth of small generating sets in SL_n(Z/pZ)

Abstract

Let G=SL_n. Let K=Z/pZ, p a prime. Let A\subset G(K) generate G(K). Suppose that |A|<p^{n+1-δ}, delta>0. Then |A A A|>>|A|^{1+ε}, where epsilon>0 and the implied constant depend only on n and delta.

arXiv comment19 pages; typos removed, some proofs shortened