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arXiv · 1001.4570

Linear Approximate Groups

Emmanuel Breuillard·Ben Green·Terence Tao
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Abstract

This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. 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 is valid for all Chevalley groups $G(\F_q)$.

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Emmanuel Breuillard, Ben Green, Terence Tao. 2010-03-15. Linear Approximate Groups. https://arxiv.org/abs/1001.4570

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