Conjugacy class

  • Thread starter Nusc
  • Start date
  • #1
753
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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?
 

Answers and Replies

  • #2
matt grime
Science Advisor
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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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