Corollary 3

Tag 02MO, permanent. Cite it as [Bourbaki, Tag 02MO].

Théories spectrales, chapter II, § 2. Classification

If G is connected, then G is divisible.

Indeed, there exists a compact connected group K and an integer $n\geqslant 0$ such that G is isomorphic to $\mathbf{R}^n\times K$ (II, p. 248, Prop. 3, where one must have L = K). Corollary 1 shows that K is divisible, and therefore G is divisible.

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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