Finite simple groups of Lie type as expanders

Alexander Lubotzky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank. The bounded rank case is deduced here from a uniform result for SL2 which is obtained by combining results of Selberg and Drinfeld via an explicit construction of Ramanujan graphs by Lubotzky, Samuels and Vishne.

Original languageEnglish
Pages (from-to)1331-1341
Number of pages11
JournalJournal of the European Mathematical Society
Volume13
Issue number5
DOIs
StatePublished - 2011

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