Corollary

Tag 04WM, permanent. Cite it as [Bourbaki, Tag 04WM].

The initial index $\varepsilon(G, H)$ divides the index $(G : H)$ and is equal to it if $G$ is isomorphic to $\mathbf{Z}$ .

In particular, $\varepsilon(G, H) \leq (G : H)$ .

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

Cited by

Nothing.