Let G be a group and Aut G the set of all automorphisms of G. (a) Aut

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Let G be a group and Aut G the set of all automorphisms of G.

(a) Aut G is a group with composition of functions as binary operation.

(b) Aut Z ≅ Z₂ and A ut Z₆≅ Z₂; Aut Z₈≅ Z₂⊕ Z₂; Aut Z_P≅ Zp^-1 (p prime).

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 13, 2023 03:07 AM

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Let G be a group and Aut G the set of all automorphisms of G. (a) Aut

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a To show that Aut G is a group we need to verify the four group axioms closure associativity identity and inverse Closure Let fg Aut G Then both f and g are automorphisms which means they are bijecti...View the full answer

Algebra Graduate Texts In Mathematics 73

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