Prove that in any group, the relation "x is a conjugate of y" is an equivalence relation. Not sure what to do here
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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 $\displaystyle a\sim b\Leftrightarrow a=gbg^{-1},\text{ }g\in G$. Reflexivity: try $\displaystyle g=e$ Symmetry: Try switching $\displaystyle g$ and $\displaystyle g^{-1}$ Transitivity: This is up to you.
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