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Math Help - Automorphisms, if it generates a group

  1. #1
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    Automorphisms, if it generates a group

    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).
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  2. #2
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    Quote Originally Posted by dabien View Post
    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).

    Ok...and what's the problem? You must show this set's closed under composition, that you have a unit and that every element there has an inverse (wrt composition, of course)....what've you done and where're you stuck?

    Tonio
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