Expansion in finite simple groups of Lie type

Emmanuel Breuillard , Ben Green , Robert Guralnick , Terence Tao

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keywords groupssimplefinitetypealgebraicbourgain-gamburdcayleycompanion

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We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper, establishing strongly dense subgroups in simple algebraic groups.

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Expansion in finite simple groups of Lie type

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