1. The problem statement, all variables and given/known data Let G be an abelian group of order n. Define phi: G --> G by phi(a) = a^m, where a is in G. Prove that if gcd(m,n) = 1 then phi is an isomorphism 2. Relevant equations phi(a) = a^m, where a is in G gcd(m,n) = 1 3. The attempt at a solution I know since G is an ableian group it is a commutative group (so ab=ba). Also since we have the special converse we know there exists a r, s \in G such that mr + ns = 1. They only way i know if proving an isomorphism is proving that it is one-to-one and onto and I'm not sure what to do with these puzzle pieces. Is there another way to prove isomorphisms?