Growth in SL3(Z/pZ)

Let G D SL3(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 vertical bar S vertical bar the number of elements of a finite set S. Assume vertical bar A vertical bar < vertical bar G vertical bar(1-epsilon) for some epsilon > 0. Then vertical bar A . A . A vertical bar > vertical bar A vertical bar(1+delta), where delta > 0 depends only on epsilon. We will also study subsets A subset of G that do not generate G. Other results on growth and generation follow.