# Equivalence of definitions of coset

From Groupprops

This article gives a proof/explanation of the equivalence of multiple definitions for the term coset

View a complete list of pages giving proofs of equivalence of definitions

## Statement

The following are equivalent for a nonempty subset of a group:

- It occurs as the Left coset of a subgroup (?).
- It occurs as the Right coset of a subgroup (?).
- Its left translates form a partition of the group.
- Its right translates form a partition of the group.