a question of symmetric group

Discussion in 'Undergraduate Math' started by winshum, Oct 1, 2006.

  1. winshum

    winshum Guest

    Let X={1,2,....n}
    Sn=S(X) and H={f be element of Sn: (n)f=n}
    Show that H is a subgroup of Sn, and which is isomorphic to S_(n-1).
    Let g be any permutation on X with (n)g=1, Find g^(-1)Hg

    winshum, Oct 1, 2006
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  2. On Sun, 01 Oct 2006 01:15:52 EDT, winshum
    I don't mean to be nasty, but this is a very straightforward
    problem. What part of it is giving you trouble?
    Suppose that h is in H. What is (1)g^(-1)hg? If you answer
    this question correctly, you should be able to find a
    subgroup K of Sn whose definition looks a lot like that of H
    and which clearly has g^(-1)Hg as a subset. With just a
    little more work you can then show that g^(-1)Hg is equal to
    this K.

    Brian M. Scott, Oct 5, 2006
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