k If f is a homomorphism of a group G into agroup G' with Kernal K. Let a&G be suchthat f(a)=a'G'. Then the set of all thoseelements of G which have the image a' in G'is the coset Ka of K in G.12:49 PM ✓

We are given that f : G → G' is a homomorphism. Kernel of f is K. => for all elements x in K,…

Answered: If f is a homomorphism of a group G…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 12E: 12. Find all homomorphic images of each group in Exercise of Section. 18. Let be the group of units...

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If f is a homomorphism of a group G into a group G' with Kernal K. Let aЄG be such that f(a)=a'=G'. Then the set of all those elements of G which have the image a' in G' is the coset Ka of K in G. 12:49 PM ✓