Definition 3

Tag 0AF9, permanent. Cite it as [Bourbaki, Tag 0AF9].

Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups

Let $G$ be a finite-dimensional connected Lie group. The Lie group $\mathrm{Int}(L(G)) = \mathrm{Ad}(G)$ is called the adjoint group of $G$ .

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

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