Finite-index subgroup quasi-isometry
= Finite-index subgroup quasi-isometry
If $H$ is a finite-index subgroup of a finitely generated group $G$, then $H$ is finitely generated and its inclusion into $G$ is a <quasi-isometry>. Finite generation follows from <Schreier's lemma>, while finitely many coset representatives give coarse surjectivity and uniformly bounded distortion.