Unifying Orders in Finite Group Conjugacy Classes

[Nusc]

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?

 

[matt grime]

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.)