Irreducible root system decomposition

Question

I am looking for the name of and a good reference on the following theorem

Theorem: let $G$ be a connected, compact and semisimple Lie group, and $T \subset G$ a maximal torus of $G$, there exists a unique collection of subtori $T_i$ in $T$ such that

1. $\prod{T_i} \to T$ is an isogeny therefore $\prod{\chi(T_i)_{\mathbb{Q}}} \hookleftarrow \chi(T)_{\mathbb{Q}}$ is an isomorphism
2. $\{(\chi(T_i)_{\mathbb{Q}}\}$ are the irreducible components of $\chi(T)_{\mathbb{Q}}$

let $G_i = Z_G(\prod_{k\neq i}{T_k})'$, the collection $\{G_i\}$ satisfy

1. $\prod{G_i} \to G$ is an isogeny
2. $G_i$'s pairwise commute
3. $G_i$ are minimal nontrivial closed connected normal subgroups of $G$, moreover every closed connected normal subgroup of $G$ is generated by some of these $G_i$'s
4. $T_i = T \cap G_i$ and are maximal tori in $G_i$ and $\Phi(G_i,T_i)$ are the weights of $\chi(T_i)_{\mathbb{Q}}$

Thank you very much!