An abelian group is a group whose operation is commutative, ie a*b=b*a An example of an abelian group is the integers with the usual addition operation An example of a group which is not abelian is the rotations of a cube (try it out) When dealing with an abelian group is it conventional to denote the group operation as addition (+), rather than multiplication (*) and to denote the unit element as 0 rather than 1