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Prove that if ct : G -+ H is a homomorphism and f3 : H -+ K is a homomorphism, thenf3 0

Chapter 21, Problem 21.11

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QUESTION:

Prove that if ct : G -+ H is a homomorphism and f3 : H -+ K is a homomorphism, thenf3 0 ct : G -+ K IS a homomorphism.

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QUESTION:

Prove that if ct : G -+ H is a homomorphism and f3 : H -+ K is a homomorphism, thenf3 0 ct : G -+ K IS a homomorphism.

ANSWER:

Step 1 of 3

Given  and be two group homomorphism.

Suppose there are two elements, since  is a group homomorphism:

According to the definition,

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