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Q1) Define the Multiplication map. Q2) Is .: Q*xQ* Q* a group homomorphism? Q3) What is the kernel of.? With what set can you

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Q1) Define the Multiplication map. Q2) Is .: Q*xQ* Q* a group homomorphism? Q3) What is the kernel of.? With what set can you identify ker. ? Q4) Is there a natural map? What is the set of cosets and with what set can you identify it? Is it a group? If yes, what is the name of this group? Q5) Define a map : Q*xQ* ker. Q*. Q6) Give the set. (Q* Q*) Q7) What theorem have you verified here? What do you get after suitable identification ? Q8) Will: NX NN, ZxZZ and. QxQQ give rise to natural maps. Why or why not?

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