2. Let o : G → G' be a homomorphism of groups, and let H be a subgroup of G. (a) Let a E G. Prove that $(a") = ¢(a)" for all n e Z. (b) Prove that if H is cyclic, then o[H] is also cyclic. (c) Prove that if H is normal in G and o is onto, then [H] is normal in G'.

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A: In order to solve this question we need to make the set of group G by finding x, y and z.

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A: Epimorphism: A homomorphism which is surjective is called Epimorphism.

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Q: 15*. Find an explicit epimorphism from Z24 onto a group of order 6. (In your work, identify the…

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