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arXiv · 1006.3365

Expansion in SL_d(Z/qZ), q arbitrary

Jean Bourgain·Péter P. Varjú
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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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Jean Bourgain, Péter P. Varjú. 2010-06-17. Expansion in SL_d(Z/qZ), q arbitrary. https://doi.org/10.1007/s00222-011-0345-4

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