Let 0:G → H be a homomorphism.Prove that ker(0) = {e} iff 0 is one-to-one.45.%3D

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Answered: 45. Let 0:G → H be a homomorphism.…

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 9E: Let be a subgroup of a group with . Prove that if and only if

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45. Let 0:G → H be a homomorphism. Prove that ker(0) = {e} iff 0 is one-to-one.