Corollary 3

Tag 0ACO, permanent. Cite it as [Bourbaki, Tag 0ACO].

Lie Groups and Lie Algebras, chapter III, § 4. Passage from Lie algebras to Lie groups

Let $G$ be a Lie group. If $L(G)$ is commutative, $G$ contains a commutative open subgroup.

There exists an open Lie subgroup germ U of G which is commutative (Corollary 2). Let V be a neighbourhood of e such that V^2 ⊂ U. Then xy = yx for all x, y in V. Hence the subgroup of G generated by V is commutative; it is obviously open.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Corollary 2