We show that every subset of SL2 (Z/pZ) grows rapidly when it acts on itself by the group operation. It follows readily that, for every set of generators A of SL2 (Z/pZ), every element of SL2 (Z/pZ) can be expressed as a product of at most O((log p)c ) elements of A ∪ A−1 , where c and the implied constant are absolute. 1. Introduction . Background. Let G be a finite group. Let A ⊂ G be a set of generators of G. By definition, every g ∈ G can be expressed as a product of elements of.
