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Definitions of abelian:
  • adjective:   (mathematics) Of an algebraic structure, having a commutative defining operation.
  • adjective:   (mathematics) Of a binary function, commutative.
  • noun:   (Roman Catholicism, historical) A member of a sect in fourth-century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel.
  • adjective:   (mathematics, group theory, dated) Alternative letter-case form of abelian [(mathematics) Of an algebraic structure, having a commutative defining operation.]

(Definitions from Wiktionary)

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