What we can say about these two elements $x= yxy^{-1} $? Let $x$ and $y$ are two elements of some group with relation $x = yxy^{-1}$. What we can say about $x$ and $y$?
I can say that $x$ and $y$ commute because $xy = yx$. What are other things we can say about $x$ and $y$? I think we can't say that $y$ is self-conjugate.
A element $x$ is said to be self conjugate if $\forall y \in G, x = yxy^{-1}$

You can say anything that follows just from the fact that they commute, and nothing else without more information.
