Let g be a cyclic group of order nSolutionGiven that G is a

Let \'g\' = be a cyclic group of order n

Solution

Given that G is a cylic group generated by g

Hence G = {g, g^2, g^3,...., g^n =e}

k is relative prime to all numbers less than or equal to n.

Definitely k has to be more than n.

Consider any element x in G

x^k = x^n * x^k-n

Since x belongs to G x = g^l, for l = 1,2,3...n.

So x^k = g^(lk)

x^(k+1) = g^(lk +l)... and so on.

Thus x^k will be generating a cyclic group of same order n.

Hence phi: G to G is isomorphic.