Corollary 2

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

Lie Groups and Lie Algebras, chapter IX, § 4. Root system associated to a compact group

Let H be a connected closed subgroup of G containing T; there is an exact sequence

0\longrightarrow N(H,T)\longrightarrow N(G,T)\longrightarrow \pi_1(H)\longrightarrow \pi_1(G)\longrightarrow 0

This follows from Algebra, Chap. X, p. 4, Prop. 2 (snake diagram), applied to the commutative diagram

0 $\longrightarrow N(H,T)\longrightarrow \Gamma (T)\longrightarrow \pi_1(H)\longrightarrow$ 0

0 $\longrightarrow N(G,T)\longrightarrow \Gamma (T)\longrightarrow \pi_1(G)\longrightarrow 0$ .

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

Algebra, Chap. X, p. 4, Prop. 2 not in this corpus: A X