Schreier's lemma
= Schreier's lemma
{c}
{wiki}
If a group $G$ is generated by $S$, a subgroup $H$ has a set $T$ of right-coset representatives, and $\overline{ts}$ denotes the representative of $Hts$, then $H$ is generated by the Schreier generators
$$
ts\overline{ts}^{-1}
\qquad(t\in T, s\in S).
$$
In particular, every finite-index subgroup of a finitely generated group is finitely generated.
= Schreier lemma
{c}
{synonym}