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Math Help - Galois Theory

  1. #1
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    Galois Theory

    Consider the automorphisms of k(x) defined by s1(x) = x (the
    identity), s2(x) = 1 - x and s3(x) = 1/x. Show that these generate a group
    G of order exactly 6 and that the remaining automorphisms are s4(x) = 1 -
    (1/x); s5(x) = 1/(1 - x), and s6(x) = x/(x - 1).

    Assuming the fundamental theorem of the Galois theory, exhibit
    all the intermediate fields between E = k(x) and F = k(I).
    I(x)= (x^2-x+1)^3 / (x^2*(x-1)^2)


    Also Show I(x) is invariant under the group G
    Last edited by dabien; November 16th 2009 at 09:08 PM.
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  2. #2
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    Quote Originally Posted by dabien View Post
    Assuming the fundamental theorem of the Galois theory, exhibit
    all the intermediate fields between E = k(x) and F = k(I).

    What is I? Is k any field? Is k(x) the field of rational functions over k?

    Tonio
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  3. #3
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    i fixed it.
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  4. #4
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    Quote Originally Posted by dabien View Post
    i fixed it.

    I don't have the slightest idea what you mean, and if you think you answered my questions then mind you: you didn't.

    Tonio
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