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
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.