(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})P^{-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,

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{}{\rightarrow}[/tex]i_{mk+1}

I don't know how to prove this last part, nor do I know if my reasoning is correct. Any suggestions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Permutation and cycles

**Physics Forums | Science Articles, Homework Help, Discussion**