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 language | English |
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Pages (from-to) | 1331-1341 |
Number of pages | 11 |
Journal | Journal of the European Mathematical Society |
Volume | 13 |
Issue number | 5 |
DOIs | |
State | Published - 2011 |