On splitting of the normalizer of a maximal torus in $E_6(q)$

Alexey Galt, Alexey Staroletov

Let $G$ be a finite group of Lie type $E_6$ over $F_q$ (adjoint or simply connected) and $W$ be the Weyl group of $G$. We describe maximal tori $T$ such that $T$ has a complement i…