A group is called cyclic group if, for some , every element is of the form , where is some integer. The element is that called generator of .
There may be more than one generators of a cyclic group. If is a cyclic group generated by , then we shall write or . The elements of will be of the form of course they are not necessarily all distinct.
(1) The multiplicative group is cyclic. The generator are and .
(2) The multiplicative group is cyclic. We can write . The generators are and .
(3) The multiplicative group of , nth roots of unity is cyclic, a generator being