Question 4: Let G be a finite abelian group of order o(G) and suppose the integer n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y". Prove that this mapping is an automorphism.
Question 4: Let G be a finite abelian group of order o(G) and suppose the integer n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y". Prove that this mapping is an automorphism.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.4: Cosets Of A Subgroup
Problem 30E: Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G...
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n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y".
Prove that this mapping is an automorphism."
Transcribed Image Text:Question 4: Let G be a finite abelian group of order o(G) and suppose the integer
n is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y".
Prove that this mapping is an automorphism.
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Algebra
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9781285463230
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Gilbert, Linda, Jimmie
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Cengage Learning,