Corollary 2

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

Let $G$ be a Lie group germ. If $L(G)$ is commutative, $G$ is locally isomorphic to the additive Lie group $L(G)$ .

The Lie algebra of the additive group $L(G)$ is isomorphic to $L(G)$ . Hence it suffices to apply Corollary 1.

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

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