All cyclic subgroups of group (U(N),.).

Recall that a group G is called cyclic if there is an element a in G such that G is equal to a to the power of n where n is integers. Such an element a is called a generator of G. If a subset H of a group G is itself a group under the operation of G, we say that H is a subgroup of G. Moreover, an integer a has a multiplicative inverse modulo n if and only if a and n are relatively prime. So, for each n>1, we define U(n) to be the set of all positive integers less than n and relatively prime to n. Then U(n) is a group under multiplication modulo n. In this article, we will using Python determine all generator of the group U(n). The result of our study shows that by using Python, for any group of U(n), we can get all their generator quickly and easily. [ABSTRACT FROM AUTHOR]