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Galois Theory question

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Let L/K be a Galois extension with Galois group isomorphic to A4. Let g(x) ϵ K [x] be an irreducible polynomial that is degree 3 that splits in L. Show that the Galois group of
    g(x) over K is cyclic.

    2. Relevant equations

    3. The attempt at a solution

    I know, Galois means normal and separable.

    Irrdeducible poly of degree 3 that splits in L means it splits into linear factors.

    ie. g(x)=(x-a1)*(x-a2)*(x-a3)

    I am thinking Galois correspondence might come in handy, but not sure how...any ideas?

    I'm not sure what information Cyclic gives.
  2. jcsd
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