ot all questions. (Total marks=20) Let G and G' be two groups. Let p: G → G' and p: G → G' be two homomorphisms then prove that H = {x € GI ¢(x) = 4(x)} is a subgroup of G. Also prove that H is a normal subgroup of G.

ot all questions. (Total marks=20) Let G and G' be two groups. Let p: G → G' and p: G → G' be two homomorphisms then prove that H = {x € GI ¢(x) = 4(x)} is a subgroup of G. Also prove that H is a normal subgroup of G.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 16E: 16. Let be a subgroup of and assume that every left coset of in is equal to a right coset of in ....

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