(Third Isomorphism Theorem) If M and N are normal subgroups ofG and N <= M, prove that (G/N)/(M/N) = G/M. Think of this as aform of “cancelling out” the N in the numerator and denominator.

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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(Third Isomorphism Theorem) If M and N are normal subgroups of
G and N <= M, prove that (G/N)/(M/N) = G/M. Think of this as a
form of “cancelling out” the N in the numerator and denominator.

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