Doubt about abelian conjugacy class

  • Thread starter frank1
  • Start date
  • #1
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Homework Statement


I'm kinda lost in the concept of conjugate elements in group theory. It says that a element "h conjugate by g" is:

g-1×h×g = hg

Then it says that if the group is abelian h = hg

Homework Equations


Abelian group: a*b = b*a

The Attempt at a Solution


I don't get why the fact that the group is abelian (a*b = b*a) leads to the conclusion that h = hg

g-1×h×g = g×h×g-1 why does it lead to h. I know it implies g×g-1 = e. But why wouldn't g-1×g = e aswell then leading to every non-abelian group also having the property h = hg?

PS: Sorry my english.
 

Answers and Replies

  • #2
746
13
if the group is abelian then it's possible to swap the ##g^{-1}## & ##h## or the ##h## & ##g## to get either ##g^{-1}g## or ##gg^{-1}## leaving h by itself.
 
  • #3
25
0
got it! thanks fourier
 

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