A Group whose group Operation is Commutativity. Axioms Group Axioms Closure: ∀A,B∈G, AB∈G Associativity: ∀A,B,C∈G, (AB)C=A(BC) Identity: ∃ I s.t. ∀A∈G, IA=AI=A Inverse: ∀ A∈G, A−1∈G s.t. AA−1=A−1A=I Commutativity Axiom Commutativity: ∀A,B∈G, AB=BA