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Let G be a cyclic group; an element g ∈ G is called a generator of...

Let G be a cyclic group; an element g ∈ G is called a generator of G if G<g>. Let φ : G → G be an endomorphism of G, and let g be a generator of G. Show that φ is an automorphism if and only if φ(g) is a generator of G. Use this to find Aut(Z).

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