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Notation. galois theory problem

  1. Mar 10, 2010 #1
    1. The problem statement, all variables and given/known data
    let [tex]K[/tex] be a field and [tex]K(t)[/tex] the rational functions in [tex]t[/tex].
    Show that [tex]\ G=Aut_K K(t)[/tex] [tex]\cong[/tex] [tex]\ GL(2,K)[/tex]

    2. Relevant equations

    I have the fundamental Galois theorem to work with and normal subgroups. but we haven't done splitting fields.

    3. The attempt at a solution
    I am really just unsure of how to proceed here. I am guessing [tex]GL(2,K)[/tex] is just the 2x2 matrices with nonzero determinants and elements in [tex]K[/tex]. and if that's true I don't really know what to do.
  2. jcsd
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