Definition 2

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

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

An element of G is said to be regular if it is regular for the adjoint representation of G.

In other words (Prop. 1), an element $g\in G$ is regular if, for all elements $g'$ in a neighbourhood of $g$ in G, the dimension of the nilspace of Ad( $g'$ ) $-1$ is equal to the dimension of the nilspace of Ad( $g$ ) $-1$ .

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

Corollary 4, § 2

Cites

Prop. 1