Finite simple groups of Lie type as expanders

  • Alexander Lubotzky

    Hebrew University, Jerusalem, Israel


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.

Cite this article

Alexander Lubotzky, Finite simple groups of Lie type as expanders. J. Eur. Math. Soc. 13 (2011), no. 5, pp. 1331–1341

DOI 10.4171/JEMS/282