论文信息 - Diameters of Cayley graphs of SL_n(Z/kZ)

Diameters of Cayley graphs of SL_n(Z/kZ)

We show that for integers k > 1 and n > 2, the diameter of the Cayley graph of SL_n(Z/kZ) associated to a standard two-element 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).

M. Kassabov | T. Riley

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