# Prove that for a general 3-cycle \sigma one can find a permutation …

I need to prove that for a general 3-cycle $\sigma$ one can find a permutation $\tau \in S_4$ such that $\tau \sigma\tau^{-1} = (123)$, and use this to show that 3-cycles in $S_4$ are even. How do i start?

I just need a hint =)

Let $\sigma=(a \, b \, c)$ be a $3$ cycle. Then you are looking at a permutation $\tau$ such that $\tau^{-1}(1 2 3)\tau=(a\, b \, c)$. Now, LHS=$(\tau^{-1}(1)\, \tau^{-1}(2)\, \tau^{-1}(3))$ (Prove this). Then can you determine $\tau$?