Resumen de Growth in Chevalley groups relatively to parabolic subgroups and some applications

Ilya D. Shkredov

• Given a Chevalley group G.q/ and a parabolic subgroup P G.q/, we prove that for any set A there is a certain growth of A relatively to P, namely, either AP or PA is much larger than A. Also, we study a question about the intersection of A n with parabolic subgroups P for large n. We apply our method to obtain some results on a modular form of Zaremba’s conjecture from the theory of continued fractions, and make the first step towards Hensley’s conjecture about some Cantor sets with Hausdorff dimension greater than 1=2