I believe you mean the generator to be . Here's a hint: any element in the first group can be represented as for some integer . Now given an element in the second group (say ), we can express . Can you figure out the rest?
Let G1 and G2 be groups, and let f: G1 -> G2 be an isomorphism.
If G1 is a cyclic group with generator a, prove that G2 is also a cyclic group, with generator f(a).
Can someone show this proof? Thanks so much!!