Remark 2

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

Lie Groups and Lie Algebras, chapter IV, § 2. Tits Systems

Suppose that Z \cap U = \{1\}. Since Z and U are normal in B, it follows that every element of Z commutes with every element of U, and hence with every element of G_1. In view of the preceding corollary, it follows that G_1 \cap Z is the centre of G_1.

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

Cited by

Nothing.

Cites

Nothing.