# "x is a conjugate of y"

• April 20th 2010, 08:12 PM
natmov85
"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(Speechless)
• April 20th 2010, 08:18 PM
Drexel28
Quote:

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(Speechless)

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.