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Nielsen–Schreier theorem

{c}

If $H$ has finite index $d$ in a <finitely generated group> $G$, then <Schreier's lemma> gives
$$
\boxed{d(H)\leq 1+d\bigl(d(G)-1\bigr).}
$$
Equality holds when $G$ is a <free group> of finite rank.

Schreier index-rank inequality

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 143 / 1 / c / Solution

Schreier index-rank inequality

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Schreier index-rank inequality

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