Integers Mod n and the Cyclic Subgroups

a

7

n

12

The group of integers modulo

n

under addition is shown as points on a circle. The red lines show the cyclic subgroup generated by the element

a

. The points on the circle are the

th

n

roots of unity, which are given by the points in the set

U

n

={z∈|

n

z

=1}

. These roots are given by the formula in the center for

m=1,2,…,n

.

Richard Hennigan