Let G be an infinite cyclic group. Prove that Aut(G)≅(Z₂,⊕).
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Hint1: Hint2: If then .
Originally Posted by hzhang610 Let G be an infinite cyclic group. Prove that Aut(G)≅(Z₂,⊕). Any homomorphism from to itself is of the form for some . This is a bijection only if . Hence there are only two automorphisms of .
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