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arXiv:math/0502221 [math.GR]AbstractReferencesReviewsResources

Diameters of Cayley graphs of SL_n(Z/kZ)

M. Kassabov, T. R. Riley

Published 2005-02-11Version 1

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).

Comments: 11 pages, no figures
Categories: math.GR, math.CO
Subjects: 20F05, 05C25, 05C35, 20D06
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