1. The problem statement, all variables and given/known data Prove that if G is a cyclic group with more than two elements, then there always exists an isomorphism: ψ: G--> G that is not the identity mapping. 2. Relevant equations 3. The attempt at a solution So if G is a cyclic group of prime order with n>2, then by Euler's function Phi(n)> 1. Then (r, n) = 1 by the definition of prime, and 1 < r < n. If G= (g), then Δ: g - > g^r is a nonidentity mapping. However, this doesn't seem like a formalized proof to me.