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  3. consider the group homomorphism ? : s3 × s5? s5 a

Consider the group homomorphism ? : S3 × S5? S5 and ?((?, ? )) = ?...

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Advance Math

Consider the group homomorphism ? : S3 ×S5? S5 and ?((?, ? )) = ? .

(a) Determine the kernel of ?. Prove your answer. Call K thekernel.

(b) What are all the left cosets of K in S3×S5 using set builder notation.

(c) What are all the right cosets of K in S3 ×S5 using set builder notation.

(d) What is the preimage of an element ? ? S5 under??

(e) Compare your answers in parts (b)-(d). What do younotice?

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