What is a Cylic group? - in group theory.........(B.sc)

Cylic group- A group G is said to be cyclic group if there exists an elements a belongs to G such that all other elements of G can obtained by taking some integeral power on a and the element a is said to be generator of the cyclic group.
For ex- If( G,*) is a group which is a set of fourth roots of unity..then,i and -i are said to be generator of the cyclic group and Group ( G,*) is said to be a cyclic group.