(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let P be a permutation of a set. Show that P(i_{1}i_{2}...i_{r})B^{-1}= (P(i_{1})P(i_{2})...P(i_{r}))

2. Relevant equations

N/A

3. The attempt at a solution

Since P is a permutation, it can be written as the product of cycles. So I figured that showing that the above equation holds for cycles will be sufficient to show that it holds for all permutations.

Let C = (i_{m1}i_{m2}...i_{mk}) be a cycle and let D = (i_{1}i_{2}...i_{r}). Then, for m_{k}[tex]\neq[/tex] r,

i_{mk}[tex]\stackrel{C^{-1}}{\rightarrow}[/tex]i_{mk-1}[tex]\stackrel{D}{\rightarrow}[/tex]i_{mk-1+1}[tex]\stackrel{C}{\rightarrow}[/tex]i_{mk+1}

Let D` = (C(i_{1})C(i_{2})...C(i_{r})), then i_{mk}[tex]\stackrel{}{D`\rightarrow}[/tex]i_{mk+1}

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Permutation and cycles

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