Diameters of Cayley graphs of Chevalley groups

M Kassabov, TR Riley

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)

Abstract

We show that for integers k >= 2 and n >= 3, the diameter of the Cayley graph of SLn (Z/kZ) associated with a standard two-element generating set is at most a constant times 112 Ink. This answers a question of A. Lubotzky concerning SLn(Fp) 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 SLn (Z/kZ). We generalize our results to other Chevalley groups over Z/kZ. (c) 2005 Elsevier Ltd. All rights reserved.
Translated title of the contributionDiameters of Cayley graphs of Chevalley groups
Original languageEnglish
Pages (from-to)791 - 800
Number of pages10
JournalEuropean Journal of Combinatorics
Volume28 (3)
DOIs
Publication statusPublished - Apr 2007

Bibliographical note

Publisher: Academic Press Ltd Elsevier Science Ltd

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