Let C be a normal subgroup of the group A and let D be a normal subgroup of the group B. Prove that (A x B) / (C x D) = (A/C) x (B/D). Hint : Show that the map phi : A x B onto (A/C) x (B/D) defined by phi(a,b) = (aC, bD) is a homomorphism 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 (A x B) / (C x D) = (A/C) x (B/D). Hint : Show that the map phi : A x B onto (A/C) x (B/D) defined by phi(a,b) = (aC, bD) is a homomorphism then use the First Isom. Thm.

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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