Let C be a normal subgroup of the group A and let D be a normal subgroup of the group B. Prove that (Cx D) <(A× B) and (Ax B)/(Cx D) = (A/C)x(B/ D). 4. Hint: Show that the map : AxB →(AIC)x(BID) defined by (a,b) = (aC,bD) is a homomorphism and then use the First Isom. Thm.

Let C be a normal subgroup of the group A and let D be a normal subgroup of the group B. Prove that (Cx D) <(A× B) and (Ax B)/(Cx D) = (A/C)x(B/ D). 4. Hint: Show that the map : AxB →(AIC)x(BID) defined by (a,b) = (aC,bD) is a homomorphism and then use the First Isom. Thm.

Name: Q4 Let C be a normal subgroup of the group A and let D be a normal sub
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Description: Q4 Let C be a normal subgroup of the group A and let D be a normal subgroup of thegroup B. Prove that (Cx D) <(A× B) and (Ax B)/(Cx D) = (A/C)x(B/ D).4.Hint: Show that the map : AxB →(AIC)x(BID) defined by(a,b) = (aC,bD) is a homomorphism and then us

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 23E

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