Expansion properties of finite simple groups
arXiv:1001.5069
Abstract
We prove that if G is SL_2(F) or PSL_2(F), where F is a finite field, and A is a set of generators of G, then either |AAA| > |A|^(1+epsilon), where epsilon is an absolute positive real number, or AAA=G. As a corollary we get that the diameter of any Cayley graph of G is Poly-Logarithmic in |G|.
PhD Thesis, The Hebrew University, September 2009, 115 pages. The results will be included in a future paper