On splitting of the normalizers of maximal tori in $E_7(q)$ and $E_8(q)$

Alexey Galt, Alexey Staroletov

Let $G$ be a finite group of Lie type $E_l$ with $l\in \{6,7,8\}$ over $F_q$ and $W$ be the Weyl group of $G$. We describe all maximal tori $T$ of $G$ such that $T$ has a complement…