Linear Approximate Groups

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 $G(\F_q)$.

11 pages. Submitted, Electronic Research Announcements. Small changes

References in corpus (5)

• Approximate groups and their applications: work of Bourgain, Gamburd, Helfgott and Sarnak
• Approximate subgroups of linear groups
• Growth in SL_3(Z/pZ)
• Growth in finite simple groups of Lie type
• Approximate groups, II: the solvable linear case

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• Freiman's theorem for solvable groups
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• Approximate subgroups of linear groups
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