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• W2953202901 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." @default.
• W2953202901 created "2019-06-27" @default.
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• W2953202901 date "2010-05-11" @default.
• W2953202901 modified "2023-09-23" @default.
• W2953202901 title "Approximate subgroups of linear groups" @default.
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• W2953202901 doi "https://doi.org/10.48550/arxiv.1005.1881" @default.
• W2953202901 hasPublicationYear "2010" @default.
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