noun
- a subset of a group formed by multiplying all elements of a subgroup by a fixed element of the group
Usage: mathematics; group theory
Examples
- The left coset of H in G is formed by multiplying each element of H by a.
- Students learned to identify cosets when studying abstract algebra.
- The cosets partition the group into disjoint subsets.
- Right cosets and left cosets may not be the same in non-abelian groups.
- The number of cosets equals the index of the subgroup.