Approximate Subgroups of Linear Groups

@article{Breuillard2010ApproximateSO,
  title={Approximate Subgroups of Linear Groups},
  author={Emmanuel Breuillard and Ben Green and Terence Tao},
  journal={Geometric and Functional Analysis},
  year={2010},
  volume={21},
  pages={774-819}
}
We establish various results on the structure of approximate subgroups in linear groups such as SLn(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 $${{\rm SL}_{n}({\mathbb {F}}_{q})}$$ which generates the group must be either very small or else nearly all of $${{\rm SL}_{n}({\mathbb {F}}_{q})}$$. The argument generalises to other absolutely almost simple connected (and… 

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