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Math Help - what are the sylow 2-subgroups of S5?

  1. #1
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    what are the sylow 2-subgroups of S5?

    what are the sylow 2-subgroups of S5?

    i know that s2=15,

    but i don't really understand how to list them.

    i also need to show they are isomorphic to a sylow 2-subgroup of S4 by showing they fix at least one element in {1,2,3,4,5}

    i'm lost, please help
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  2. #2
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    Quote Originally Posted by Louise View Post
    what are the sylow 2-subgroups of S5?

    i know that s2=15,

    but i don't really understand how to list them.

    i also need to show they are isomorphic to a sylow 2-subgroup of S4 by showing they fix at least one element in {1,2,3,4,5}

    i'm lost, please help

    <(12)(34),(1234)\;;\; \left((12)(34)\right)^2=(1234)^4=1\,,\,(12)(34)(12  34)(12)(34)=(1432)>...do you recognize this group?

    Tonio
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