Definitions for

**"Abelian group"**group in which the operation is commutative.

An abelian group is a group whose operation is commutative, ie *=*. 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.

a group that satisfies the commutative law