#mathematical_group__group  a set that is closed, associative, has an identity element and every element has an inverse
  supertype:  set  (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite"
  subtype:  subgroup.mathematical_group  (mathematics) a subset (that is not empty) of a mathematical group
  subtype:  Abelian_group__commutative_group__commutativegroup  a group that satisfies the commutative law

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