论文标题
与抛物线亚组相对的雪佛兰组的增长和某些应用
Growth in Chevalley groups relatively to parabolic subgroups and some applications
论文作者
论文摘要
给定一个Chevalley组$ {\ Mathbf G}（Q）$和抛物线子组$ P \ subset {\ Mathbf G}（q）$，我们证明，对于任何集合$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ ap $ ap $ ap $ ap $ ap $ ap $ ap $ ap $ ap $ a $ a $ a $ a $ a $ a $ a。此外，我们研究了一个关于$ a^n $与抛物线子组$ p $的问题。我们采用我们的方法来从Zaremba的模块化形式中从持续分数的理论中获得一些结果，并迈出了Hensley对Hausdorff Dimension的某些Cantor Sets的猜想的第一步，该猜想的构想大于$ 1/2 $。
Given a Chevalley group ${\mathbf G}(q)$ and a parabolic subgroup $P\subset {\mathbf G}(q)$, 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 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 $1/2$.
