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
phi(a) = a^m, where a is in G
gcd(m,n) = 1
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?