Abelian Group

A type of group in which the element can also be related to each other in pairs by a communicative operation. For example, if the operation is mutiplication,and the elements are rational numbers, than the set is an abelian group because for any two elements a,b and a*b = b*a,and all these numbers, a,b and a*b are elements in the set. All cycle groups are Abelian groups.