We show that pairs of generators for the family Sz() of Suzuki groups may be selected so that the corresponding Cayley graphs are expanders. By combining this with several deep works of Kassabov, Lubotzky and Nikolov, this establishes that the family of all non-abelian finite simple groups can be made into expanders in a uniform fashion.
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Emmanuel Breuillard, Ben J. Green, Terence Tao, Suzuki groups as expanders. Groups Geom. Dyn. 5 (2011), no. 2, pp. 281–299DOI 10.4171/GGD/128