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 ZP ≅ Zp-1 (p prime).
(c) What is Aut Zn for arbitrary n ϵ N*?
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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
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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