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An automorphism of a group G is an isomorphism from G to G. The set of...

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Advance Math

An automorphism of a group G is an isomorphism from G to G. Theset of all automorphisms of G forms a group Aut(G), where the groupmultiplication is the composition of automorphisms. The groupAut(G) is called the automorphism group of group G.

(a) Show that Aut(Z) ≃ Z2. (Hint: consider generators of Z.)

(b) Show that Aut(Z2 × Z2) ≃ S3.

(c) Prove that if Aut(G) is cyclic then G is abelian.

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