Some cyclic groups have an infinite number of elements. In these groups, for every non-zero element ⁠ a ⁠, all the powers of a are distinct; despite the name "cyclic group", the powers of the elements do not cycle. An infinite cyclic group is isomorphic to ⁠ ( Z , + ) ⁠, the group of integers under addition introduced above. As these two prototypes are both abelian, so are all cyclic groups.