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## Homework Statement

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.

## Homework Equations

## 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.