Geodesic
Finite simple groups of Lie type as expanders
Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1331-1341

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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.
DOI : 10.4171/jems/282
Classification : 00-XX
Keywords: 
Alexander Lubotzky. Finite simple groups of Lie type as expanders. Journal of the European Mathematical Society, Tome 13 (2011) no. 5, pp. 1331-1341. doi: 10.4171/jems/282
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     author = {Alexander Lubotzky},
     title = {Finite simple groups of {Lie} type as expanders},
     journal = {Journal of the European Mathematical Society},
     pages = {1331--1341},
     year = {2011},
     volume = {13},
     number = {5},
     doi = {10.4171/jems/282},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/282/}
}
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