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arxiv: 1006.3365 · v1 · submitted 2010-06-17 · 🧮 math.GR · math.CO· math.DS

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Expansion in SL_d(Z/qZ), q arbitrary

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classification 🧮 math.GR math.COmath.DS
keywords arbitraryassumecayleyexpandersexpansionfamilyfinitefixed
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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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