Corollary 3

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

Lie Groups and Lie Algebras, chapter IX, § 5. Conjugacy classes

Let H be a Lie group and $\Gamma$ a compact subgroup of H. Assume that $H_0$ is compact and that $\Gamma$ satisfies condition (*) of Cor. 2. Then there exists a maximal torus T of $H_0$ such that $\Gamma \subset N_H(T)$ .

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

Corollary 4, § 5

Cites

Cor. 2