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We can traverse all elements of a group G by constructing cosets using a subgroup H. By multiplying every element g in G with the subgroup H (forming left cosets gH or right cosets Hg), the union of all distinct cosets covers every element of G exactly once.

Conditions: G is a group; H is a subgroup of G

We can traverse all elements of a group G by constructing cosets using a subgroup H. By multiplying every element g in G with the subgroup H (forming left cosets gH or right cosets Hg), the union of all distinct cosets covers every element of G exactly once.

Conditions: G is a group; H is a subgroup of G