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Math Help - Conjugates of elements in a group

  1. #1
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    Conjugates of elements in a group

    Hey, How do I find the conjugate classes of a dihedral group of order 2n?

    And in Sn what is the number of r cycles? I thought it was nCr, but I have been asked to prove it is n!/(r((n-r)!)) ?
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  2. #2
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    Oh wait, that r cycles question..

    I can choose elements in nCr ways.
    Out of these I fix the least element in the first place. So that there are (r-1) ways to fill the 2nd place and so on. i.e. the cycle say (5,2,7) is replaced by (2,7,5). So ther are (r-1)! ways of doing this. So the total no. of ways is nCr * (r-1)! which is the reqd. nswer.

    Am I right?
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  3. #3
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by poorna View Post
    Hey, How do I find the conjugate classes of a dihedral group of order 2n?
    What do elements of D_{2n} look like? So, take an arbitrary element in this form, and conjugate it by another arbitrary element, y^{-1}xy. What does this element look like?

    Such elements form your conjugacy class.
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