1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Cyclic extension

  1. Oct 14, 2008 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations

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

    3. The attempt at a solution
  2. jcsd
  3. Oct 14, 2008 #2


    User Avatar

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook