Consider ζn = exp(2π√−1/n) ∈ C for n ∈ N. (a) Find [Q(ζn) : Q] (b) FIND {Q(ζn) : Q} (c) FIND Aut(Q(ζn)/Q)

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Consider ζn = exp(2π√−1/n) ∈ C for n ∈ N. (a) Find [Q(ζn) : Q] (b) FIND {Q(ζn) : Q} (c) FIND Aut(Q(ζn)/Q) and JUSTIFY your answer. (d) Prove or Disprove Aut(Q(ζn)/Q) is always cyclic. (e) Given a diagram consisting of all subfields of Q(ζ6) containing Q, i.e., all intermediate fields between Q(ζ6) and Q, AND JUSTIFY your answer. [Hint: Galois Theory]
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