Corollary 2

Tag 01A5, permanent. Cite it as [Bourbaki, Tag 01A5].

Lie Groups and Lie Algebras, chapter IX, § 2. Maximal tori of compact Lie groups

The intersection of the maximal tori of G is the centre of G.

Let $x$ be an element of the centre of G; by Th. $2c)$ , there exists a maximal torus T of G containing $x$ ; then $x$ belongs to all the conjugates of T, hence to all the maximal tori of G. Conversely, if $x$ belongs to all the maximal tori of G, it commutes with every element of G by Th. $2c)$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Proposition 1, § 2
Corollary 3, § 2
Corollary 5, § 2
Proposition 8, § 4

Cites

Nothing.