Group (mathematics)
In the groups Z/nZ introduced above, the element 1 is primitive, so these groups are cyclic. Indeed, each element is expressible as a sum all of whose terms are 1. Any cyclic group with n elements is isomorphic to this group. A second example for cyclic groups is the group of n-th complex roots of unity, given by complex numbers z satisfying zn = 1. These numbers can be visualized as the vertices on a regular n-gon, as shown in blue at the right for n = 6. The group operation is multiplication of complex numbers. In the picture, multiplying with z corresponds to a counter-clockwise rotation by 60deg. Using some field theory, the group Fpx can be shown to be cyclic: for example, if p = 5, 3 is a generator since 31 = 3, 32 = 9  4, 33  2, and 34  1.
What group is isomorphic to cyclic groups?
Any cyclic group with n elements
Any cyclic group with n elements is isomorphic to this group.
cyclic groups