Groups, Geometry, and Dynamics

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Volume 5, Issue 2, 2011, pp. 281–299
DOI: 10.4171/GGD/128

Suzuki groups as expanders

Emmanuel Breuillard[1], Ben J. Green[2] and Terence Tao[3]

(1) Laboratoire de Mathématiques, Université Paris-Sud 11, Bâtiment 425, 91405, ORSAY CEDEX, FRANCE
(2) Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG, OXFORD, UNITED KINGDOM
(3) Department of Mathematics, University of California Los Angeles, 405 Hilgard Avenue, CA 90095-1555, LOS ANGELES, UNITED STATES

We show that pairs of generators for the family Sz($q$) 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.

Keywords: Expanders, Suzuki group, additive combinatorics

Breuillard Emmanuel, Green Ben, Tao Terence: Suzuki groups as expanders. Groups Geom. Dyn. 5 (2011), 281-299. doi: 10.4171/GGD/128