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Homework Help: Conjugacy class

  1. Sep 30, 2006 #1
    Show that the
    elements in a conujgacy class of a
    finite group all have the same order

    cl(a) = {xax^-1|x in G} G is finite
    G = {e,g1,g2,...,gm}

    cl(g)={e,c1,c2,c3,...,cn} finite for n =< m

    Then |e| | n , |c1| | n, |c2| | n, |cn| | n

    Well C1 =xgix^1 for some gi.

    any hint?
  2. jcsd
  3. Oct 1, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    What is the definition of order of an element? And I don't mean for you to just post it here, I mean for you to go from that and think about things: if x^n=e what can you say about n relative to the order of e?

    (That the conjugacy class sizes divide the order of the group is immaterial.)
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