Remark 1

Tag 01DZ, permanent. Cite it as [Bourbaki, Tag 01DZ].

Lie Groups and Lie Algebras, chapter IX, § 5. Conjugacy classes

The group $H_A$ can be identified naturally with $\Gamma (T)/N(G,T)$ , hence also with $\pi_1(G)$ . Thus, it reduces to the identity element when G is simply-connected.

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.

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