(3) Show that there does not exist a surjective (i.e., onto) homomorphism f : Sn ? Cp for any integer n ? 2 and any prime number p ? 3. Here Cp denote the cyclic group of order p.Hint: The cases, where n = 2, 3 and 4 require special care.
Suppose that G = hai. Then I claim that ha i i = G if and only if i is relatively prime to n. This
will indeed finish the problem, since there exactly ?(n) positive integers i < n with this...
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Oct 14, 2020EXPERT
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