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Math Help - Symmetric group

  1. #1
    Junior Member ibnashraf's Avatar
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    Symmetric group

    Question:

    What are the orders of the Sylow p-subgroups of the symmetric group S_6?
    Give the possible orders of each Sylow p-subgroup of S_6.
    (N.B. If there are many possible orders, then give at least four).


    Can anyone help me to understand what is meant by the above question please?

    So far i understand that S_6 is the symmetric group of degree 6.
    that is the symmetric group on { {1,2,3,4,5,6} }
    and i think that the order is given by 6!.
    where do i go from there?
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  2. #2
    MHF Contributor

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    Re: Symmetric group

    the primes dividing 6! are 2,3, and 5 (7 is too big).

    the prime factorization of 6! = 720 is: (24)(32)(5).

    the sylow 2-subgroups are all of order 16.

    the sylow 3-subgroups are all of order 9.

    the sylow 5-subgroups are all of order 5.
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  3. #3
    Junior Member ibnashraf's Avatar
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    Re: Symmetric group

    Thanks alot Deveno .... i finally understand how to go about finding Sylow p-subgroups now.
    my lecture notes in class wasn't to clear on this ....
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