Equivalence of definitions of coset

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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:

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