Usually means: Commutative under a binary operation.
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We found 15 dictionaries that define the word abelian:

General (13 matching dictionaries)
  1. abelian: Merriam-Webster
  2. abelian: Oxford Learner's Dictionaries
  3. Abelian: Collins English Dictionary
  4. Abelian, abelian: Wordnik
  5. Abelian, abelian: Wiktionary
  6. Abelian: Infoplease Dictionary
  7. Abelian, abelian: Dictionary.com
  8. Abelian: Wikipedia, the Free Encyclopedia
  9. Abelian: Online Plain Text English Dictionary
  10. Abelian: AllWords.com Multi-Lingual Dictionary
  11. abelian: FreeDictionary.org
  12. Abelian: TheFreeDictionary.com
  13. abelian: Merriam-Webster

Science (2 matching dictionaries)
  1. Abelian: Eric Weisstein's World of Mathematics
  2. abelian, abelian: PlanetMath Encyclopedia

Definitions from Wiktionary (Abelian)

adjective:  (mathematics) Of an algebraic structure (usually a group or algebra), having a commutative defining operation.
adjective:  (mathematics) Of a binary function, commutative.
noun:  (Christianity, 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 (usually a group or algebra), having a commutative defining operation.]

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