Corollary

Tag 00W5, permanent. Cite it as [Bourbaki, Tag 00W5].

Lie Groups and Lie Algebras, chapter VII, § 4. Regular elements of a Lie group

Let $G^*$ be an open subgroup of G. If $a\in G$ is regular, there exists a neighbourhood V of $a$ such that, for all $a'\in V,\mathfrak{g}^1(a')$ is conjugate to $\mathfrak{g}^1(a)$ under Ad( $G^*$ ).

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

Proposition 8, § 4

Cites

Nothing.