Expansion in SL_d(Z/qZ), q arbitrary

Details Expansion in SL_d(Z/qZ), q arbitrary Expansion in SL_d(Z/qZ), q arbitrary

2010-06-17

arxiv.org/abs/1006.3365v1

Mathematics

Group Theory

Scientific paper

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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