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Expansion in SL_d(Z/qZ), q arbitrary

Published 17 Jun 2010 in math.GR, math.CO, and math.DS | (1006.3365v1)

Abstract: Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G) with respect to the generating set pi_q(S) form a family of expanders, where pi_q is the projection map Z->Z/qZ.

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