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Assume is finite. For construct . Then, .

There are two solutions to in the multiplicative group but only one solution to in the additive one.Q2:Prove that (Q,+) is not isomorphic to (Q,*)?

If is infinite and then define by as the isomorphism. Be sure to argue this is well-defined.Q3:Prove that a cyclic group is isomorphic either to (Zn,+) for some positive integer n or to (Z,+) ?

If is finite and with then define by . Be sure to argue this is well-defined.