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Cyclic extension

  • Thread starter PIM
  • Start date
  • #1
PIM
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Homework Statement


Let K be a field, and let K' be an algebraic closure of K. Let sigma be
an automorphism of K' over K, and let F be the fix field of sigma. Let L/F
be any finite extension of F.


Homework Equations



Show that L/F is a finite Galois extension whose
Galois group Gal(L/F) is cyclic.

The Attempt at a Solution

 

Answers and Replies

  • #2
PIM
2
0
I thought about the prime subfiled of F, which is isomorphic to F_p or Q, and tried to prove that L is finite Galois over this prime subfield. (but failed) if I could show this, then it's obvious that L is finite galois over F since F is an intermediate field.

But for the cylic galois group, I still haven't got any idea.
 

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