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P-Sylow subgroup

  1. Nov 22, 2009 #1
    1. The problem statement, all variables and given/known data
    S4xZ/5

    Find the number of p-Sylow subgroups for p=2, 3, and 5


    3. The attempt at a solution

    S4 is no problem. There I can use some binomial coefficients and count stuff. I was wondering how to tackle any Z/n.

    2-Sylow

    First we find 2-sylow subgroups of S4. [tex]\frac{\binom{4}{2}*2!}{2}[/tex] or 3.

    Now I'm stuck, are the 2-Sylow subgroups of Z/5 just elements of order 2. I don't think there are any.
     
  2. jcsd
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