Diameters of Cayley graphs of SL_n(Z/kZ)

Details Diameters of Cayley graphs of SL_n(Z/kZ) Diameters of Cayley graphs of SL_n(Z/kZ)

2005-02-11

arxiv.org/abs/math/0502221v1

Mathematics

Group Theory

11 pages, no figures

Scientific paper

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).

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