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Homework Help: Permutation Group

  1. Sep 3, 2010 #1
    1. The problem statement, all variables and given/known data

    I have problems understanding part (f) of the following worked example:

    [PLAIN]http://img7.imageshack.us/img7/5557/61793282.gif [Broken]

    3. The attempt at a solution

    So in part (f), when calculating [tex](\sigma \tau)^{9000}[/tex], how does [tex](\sigma \tau)^{818 \times 11} (\sigma \tau)^2[/tex] reduce to [tex](\sigma \tau)^2[/tex]? What happens to the [tex](\sigma \tau)^{818 \times 11}[/tex] part?

    Similarly in [tex](\sigma \tau)^{-21}=(\sigma \tau)^{-2 \times 11} (\sigma \tau)^1 = (\sigma \tau)^1[/tex]

    why has the "[tex](\sigma \tau)^{-2 \times 11}[/tex]" been omitted?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 3, 2010 #2

    Office_Shredder

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    What is [tex](\sigma \tau)^11[/tex] equal to? Hint: You know that it has order 11
     
  4. Sep 6, 2010 #3
    Well, [tex](\sigma \tau)^{11}=e[/tex] where e is the identity. But what happens to the [tex](\sigma \tau)^{-2}[/tex]? Why does the "-2" disappear (since anything multiplied by the identity is itself)?
     
  5. Sep 6, 2010 #4

    Office_Shredder

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    [tex](\sigma \tau)^{-2 \times 11} = ((\sigma \tau)^{11})^{-2}[/tex]
     
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