abelian group /əˈbi.li.ən ɡɹup/ noun1 •A group in which the group operation is commutative.Let G and H be partially ordered abelian groups. A positive homomorphism from G to H is any abelian group homomorphism f:G→H that maps positive elements to positive elements, that is, f(G⁺)⊆H⁺. — 1986 formsAbelian groups · abelian groups