Coset

Symbol-free definition
A subset of a group is said to be a coset if it satisfies the following equivalent conditions:


 * It occurs as a left coset of some subgroup, or equivalently, its left quotient is a subgroup
 * It occurs as a right coset of some subgroup, or equivalently, its right quotient is a subgroup
 * The translates of the subset under left multiplication by elements of the group, are pairwise disjoint and form ap artition of the whole group
 * The translates of the subset under right multiplication by elements of the group, are pairwise disjoint, and form a partition of the whole group.

Stronger properties

 * Subgroup

Related properties

 * Double coset

Links to related riders

 * Google groups discussion on left coset being the same as right coset