Corollary 1

Tag 01A3, permanent. Cite it as [Bourbaki, Tag 01A3].

Lie Groups and Lie Algebras, chapter IX, § 2. Maximal tori of compact Lie groups

a) The exponential map of G is surjective.

b) For all $n\geq 1$ , the map $g \rightarrow g^n$ from G to itself is surjective.

Indeed, exp(L(G)) contains all the maximal tori of G, hence a). Assertion b) follows from the formula (exp $x$ ) $^n=$ exp $nx$ for $x$ in L(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.

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