Automorphism, Abelian Group and GCD

Let G be a finite Abelian group of order n, and let m be a positive integer with gcd(m,n)=1. Prove that φ:G-->G defined by φ(g)=g^m for all g an element of G belongs to Aut(G).

Solution Summary

Automorphism, Abelian Group and GCD are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.