Finite simple groups of Lie type as expanders

Alexander Lubotzky

Type: Article

Publication Date: 2011-07-13

Citations: 23

DOI: https://doi.org/10.4171/jems/282

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.

Locations

Journal of the European Mathematical Society - View - PDF

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Works Cited by This (16)

Action	Title	Year	Authors
+	The Classification of the Finite Simple Groups	1994	Daniel Gorenstein Richard Lyons Ronald Solomon
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+	The Classification of the Finite Simple Groups	1980	Michael Aschbacher
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