If psi is homomorphism of group G onto G bar with kernal K and N bar is a normal subgroup of G bar. N={x£G|psi(x)£N bar}: Then prove that G/N=G bar/N and G/N= (G/K)/(N/K)

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 34E
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If psi is homomorphism of group G onto G bar with kernal K and N bar is a normal subgroup of G bar.

N={x£G|psi(x)£N bar}:

Then prove that G/N=G bar/N and G/N= (G/K)/(N/K)

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