Finite-index subgroup
= Finite-index subgroup
A subgroup $H\leq G$ has finite index when the coset space $G/H$ is finite. Intersecting a finite-index subgroup with a subgroup again gives a finite-index subgroup of the latter.
= Finite-index subgroup
A subgroup $H\leq G$ has finite index when the coset space $G/H$ is finite. Intersecting a finite-index subgroup with a subgroup again gives a finite-index subgroup of the latter.