
Diameters of Cayley Graphs of Chevalley Groups Martin Kassabov and Tim Riley Eur. J. Comb., 28(3), pages 791–800, April 2007 We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SL_{n}(Z/kZ) with respect to a standard twoelement generating set, is at most a constant times n^{2} ln k. This answers a question of A. Lubotzky concerning SL_{n}(F_{p}) and is unexpected because these Cayley graphs do not form an expander family. Our proof amounts to a quick algorithm for finding short words representing elements of SL_{n}(Z/kZ). We generalize our results to other Chevalley groups over Z/kZ.
