Editing Coset (section)

=== Index of a subgroup ===
{{Main|Index of a subgroup}}
Every left or right coset of {{math|''H''}} has the same number of elements (or [[cardinality]] in the case of an [[Infinity|infinite]] {{math|''H''}}) as {{math|''H''}} itself. Furthermore, the number of left cosets is equal to the number of right cosets and is known as the '''index''' of {{math|''H''}} in ''G'', written as {{math|[''G'' : ''H'']}}. [[Lagrange's theorem (group theory)|Lagrange's theorem]] allows us to compute the index in the case where {{math|''G''}} and {{math|''H''}} are finite:
<math display="block">|G| = [G : H]|H|.</math>
This equation can be generalized to the case where the groups are infinite.