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Let S be a fixed finite symmetric subset of SL_d(Z), and assume that itgenerates 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, wherepi_q is the projection map Z->Z/qZ.

Expansion in SL_d(Z/qZ), q arbitrary