Diameters of Cayley graphs of SL_n(Z/kZ)

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dc.creatorKassabov, M.
dc.creatorRiley, T. R.
dc.date2005-02-11
dc.date.accessioned2026-07-07T05:16:53Z
dc.date.available2026-07-07T05:16:53Z
dc.descriptionWe 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).
dc.description11 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0502221
dc.identifierhttp://arxiv.org/abs/math/0502221
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74151
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subjectprimary 20F05; secondary 05C25, 05C35, 20D06
dc.titleDiameters of Cayley graphs of SL_n(Z/kZ)
dc.typetext

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