1. The problem statement, all variables and given/known data 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 2. Relevant equations Abelian group: a*b = b*a 3. 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.