Corollary

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

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

The set S consists of the elements $w \in W$ such that $w \neq 1$ and $B \cup C(w)$ is a subgroup of G.

The elements $w \in W$ such that $B \cup C(w)$ is a subgroup of G are those for which there exists $X \subset S$ with $W_X = \{1, w\}$ . Moreover, if $w \neq 1$ , we necessarily have Card(X) = 1 , i.e. $w \in S$ .

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

Cited by

Remark 1, § 2

Cites

Nothing.