Definition of abelian:
(adj) :
(mathematics) Of an algebraic structure (usually a group or algebra), having a commutative defining operation.
(adj) :
(mathematics) Of a binary function, commutative.
(n) :
(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.
(adj) :
(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.]