 Coset

For a subgroup $H\le G$, a left coset is $gH=\{gh:h\in H\}$. The left cosets partition $G$ and all have cardinality $|H|$.

In group theory, which is a branch of abstract algebra, a **coset** is a concept used to describe a way of partitioning a group into smaller, equally structured subsets. Cosets arise when considering a subgroup within a larger group.