Let $p$ be a prime number, and let $k=\mathbb{F}_p$ be the field of $p$ elements. Let $G=GL_n(k)$. We know that $$|G|=\prod_{i=0}^{n-1}(p^n-p^i)=p^{\binom{n}{2}}\prod_{i=0}^{n-1}(p^{n-i}-1)$$ so that the Sylow $p$-subgroups of $G$ have order $p^{\binom{n}{2}}$. One such subgroup is $U$, the upper-triangular unipotent subgroup consisting of all upper-triangular matrices with $1$’s on the diagonal. Let $A_{ij}=I_n+E_{ij}$ for $j>i$, where […]

I need some information about the Sylow $p$-subgroups, and their normalizers, (specially their sizes), of a finite simple group of Lie type over a finite field (not necessarily algebraic closed) of characteristic $p$. I would really be appreciate being introduced to a good reference or to be given some information directly.

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