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Exercise 7.4. Let N₁ and №2 be normal subgroups of groups G₁ and G2, respectively. Show that N₁N2 is a normal subgroup of G₁ ×G2 and (G1×G2)/(N₁×N2) is isomorphic to (G₁/N₁)×(G2/N2).

Exercise 7.4. Let N₁ and №2 be normal subgroups of groups G₁ and G2, respectively. Show that N₁N2 is a normal subgroup of G₁ ×G2 and (G1×G2)/(N₁×N2) is isomorphic to (G₁/N₁)×(G2/N2).

Elements Of Modern Algebra
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 21E: With H and K as in Exercise 18, prove that K is a normal subgroup of HK. Exercise18: If H is a...
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Exercise 7.4. Let N₁ and №2 be normal subgroups of groups G₁ and G2, respectively. Show that N₁N2 is a normal subgroup of G₁ ×G2 and (G1×G2)/(N₁×N2) is isomorphic to (G₁/N₁)×(G2/N2).
Transcribed Image Text:Exercise 7.4. Let N₁ and №2 be normal subgroups of groups G₁ and G2, respectively. Show that N₁N2 is a normal subgroup of G₁ ×G2 and (G1×G2)/(N₁×N2) is isomorphic to (G₁/N₁)×(G2/N2).
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