Corollary 3

Tag 019L, permanent. Cite it as [Bourbaki, Tag 019L].

Lie Groups and Lie Algebras, chapter IX, § 1. Compact Lie algebras

The fundamental group of a connected compact Lie group G is a $\mathbf{Z}$ -module of finite type, of rank equal to the dimension of C(G).

Indeed, with the notations in Cor. 1, the fundamental group of $C(G)_0$ is isomorphic to $\mathbf{Z}^n$ , with $n=$ dim $C(G)_0$ , and the fundamental group of D(G) is finite (Cor. 2).

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

Nothing.

Cites

Cor. 1
Cor. 2