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Prove that every quotient group of an Abelian group is Abelian

Chapter 22, Problem 22.5

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QUESTION:

Prove that every quotient group of an Abelian group is Abelian.

Questions & Answers

QUESTION:

Prove that every quotient group of an Abelian group is Abelian.

ANSWER:

Step 1 of 2

Let be a subgroup of an abelian group

From the properties of abelian group;

Every subgroup of an abelian group is normal.

So,  is the normal subgroup of .

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