I’m reading Humphrey’s Linear Algebraic Group. Here is a Corollary in 21.3:
Let $\phi:G \rightarrow H$ be a surjective morphism of linear algebraic groups. Let $T \subset G$ be a maximal torus: how to show that $\phi(T)$ is also a maximal torus and all the maximal Tori are obtained in this way?
I know that this statement holds for Borel subgroups of $G$, and the maximal tori of $G$ are those of Borel subgroups of $G$. But I do not know how to do next…