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arXiv · 1005.1881

Approximate subgroups of linear groups

Emmanuel Breuillard·Ben Green·Terence Tao
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Abstract

We establish various results on the structure of approximate subgroups in linear groups such as SL_n(k) that were previously announced by the authors. For example, generalising a result of Helfgott (who handled the cases n = 2 and 3), we show that any approximate subgroup of SL_n(F_q) which generates the group must be either very small or else nearly all of SL_n(F_q). The argument generalises to other absolutely almost simple connected (and non-commutative) algebraic groups G over a finite field k. In a subsequent paper, we will give applications of this result to the expansion properties of Cayley graphs.

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Emmanuel Breuillard, Ben Green, Terence Tao. 2010-05-11. Approximate subgroups of linear groups. https://arxiv.org/abs/1005.1881

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