# Finite index subgroups of infinite groups

I want to use the following Theorem:

If $H\leq U\leq G$ are (maybe) infinite groups. And $|U:H|<\infty$, $|G:U|<\infty$. Then

$|G:H|=|G:U|\cdot |U:H|$.

I think, i could proof it, but i don't want to proof it. I only need a reference.

Thanks for help.

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This is in Robinson's book A Course in the Theory of Groups. It is on page $11$ ($1.3.5$).