Coset

Summary

In mathematics, specifically group theory, a subgroup $H$ of a group $G$ may be used to decompose the underlying set of $G$ into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets (both left and right) have the same number of elements (cardinality) as does $H$. Furthermore, $H$ itself is both a left coset and a right coset. The number of left cosets of $H$ in $G$ is equal to the number of right cosets of $H$ in $G$. This common value is called the index of $H$ in $G$ and is usually denoted by $[G : H]$.