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Homework Help: Galois Theory - relations

  1. Jan 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let L = Q(t) be the field of rational functions with one variable over Q. Consider the field automorphisms of L defined by a : t -> 1 - t and b : t -> 1/t . Find the relations.

    I will then be using this to find the size and abstract structure of the subgroup G of Aut(L) generated by a and b. But for now, my question is what does it mean by find the relations?

    2. Relevant equations



    3. The attempt at a solution

    The only relations I can think of are equivalence relations. All I have managed to do with these automorphisms is work out a^2 = id and b^2 = id.
     
  2. jcsd
  3. Jan 13, 2012 #2
    Work out

    b
    ba
    bab
    baba
    babab
    bababa
    ...

    Until you get the identity (or something familiar)
     
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