Definition of "abelian"

abelian

/əˈbi.li.ən/

adjective
not comparable
1. (mathematics) Of an algebraic structure, having a commutative defining operation.
  Quotations
  The interesting aspect here is that U3 is irreducible, even though all irreps over the complexes are one-dimensional because ℤ4 is abelian.
  1996, Barry Simon, Representations of Finite and Compact Groups, page 50
2. (mathematics) Of a binary function, commutative.