Question 4: Let G be a finite abelian group of order o(G) and suppose the integern is relatively prime to o(G). Consider the mapping : G→G defined by (y) = y".Prove that this mapping is an automorphism.

Answered: Question 4: Let G be a finite abelian…

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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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.