grandes-ecoles 2020 Q21

grandes-ecoles · France · centrale-maths1__mp Groups Symmetric Group and Permutation Properties
We consider, in this question only, $n = 7$ and the cycles $\gamma_1 = (1\;3)$ and $\gamma_2 = (2\;6\;4)$. We also consider a permutation $\rho \in \mathfrak{S}_7$ such that $\rho(1) = 2, \rho(3) = 6$ and $\rho(7) = 4$. Verify that $\rho \gamma_1 \rho^{-1} = \gamma_2$. 
We consider, in this question only, $n = 7$ and the cycles $\gamma_1 = (1\;3)$ and $\gamma_2 = (2\;6\;4)$. We also consider a permutation $\rho \in \mathfrak{S}_7$ such that $\rho(1) = 2, \rho(3) = 6$ and $\rho(7) = 4$. Verify that $\rho \gamma_1 \rho^{-1} = \gamma_2$.
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