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arXiv · 1407.3158

Approximate subgroups and super-strong approximation

Emmanuel Breuillard
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Abstract

Surveying some of the recent developments on approximate subgroups and super-strong approximation for thin groups, we describe the Bourgain-Gamburd method for establishing spectral gaps for finite groups and the proof of the classification of approximate subgroups of semisimple algebraic groups over finite fields. We then give a proof of the super-strong approximation for mod $p$ quotients via random matrix products and a quantitative version of strong approximation. Some applications to the group sieve are also presented.

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Emmanuel Breuillard. 2014-07-11. Approximate subgroups and super-strong approximation. https://arxiv.org/abs/1407.3158

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