# Thread: "x is a conjugate of y"

1. ## "x is a conjugate of y"

Prove that in any group, the relation "x is a conjugate of y" is an equivalence relation.

Not sure what to do here

2. Originally Posted by natmov85
Prove that in any group, the relation "x is a conjugate of y" is an equivalence relation.

Not sure what to do here
I assume you are talking about conjugacy classes $a\sim b\Leftrightarrow a=gbg^{-1},\text{ }g\in G$.

Reflexivity: try $g=e$

Symmetry: Try switching $g$ and $g^{-1}$

Transitivity: This is up to you.