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Thread: Number of conjugacy classes

  1. April 10th 2011, 01:41 AM #1
    doug
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    Number of conjugacy classes

    Show that the number of conjugacy classes in a finite group equals the average of the orders of the centralizers of elements.

    Any help would be appreciated!
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  2. April 10th 2011, 02:52 AM #2
    tonio
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    Quote Originally Posted by doug View Post
    Show that the number of conjugacy classes in a finite group equals the average of the orders of the centralizers of elements.

    Any help would be appreciated!


    You may want to google for the most general result, Burnside's Lemma in actions of groups.

    Tonio
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