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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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.
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