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Finding cycles

  1. Mar 4, 2015 #1
    1. The problem statement, all variables and given/known data
    Let α = (α1α2...αs) be a cycle, for positive integers α1α2...αs. Let π be any permutation that παπ-1 is the cycle (π(α1)πα2...π(αs)).

    2. Relevant equations


    3. The attempt at a solution
    I started by choosing a specific α and π, and tried finding παπ-1 to give myself some idea of what to do but have had no luck. Suggestions would be welcomed.
     
  2. jcsd
  3. Mar 4, 2015 #2

    Dick

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    For example, work out what is ##\pi \alpha \pi^{-1}(\pi(\alpha_1))##?
     
  4. Mar 4, 2015 #3
    I would get παπ−1(π(α1)) = πα(α1)) = πα2?
    It gives me the next element in the cycle. So παπ−1 would be that cycle.
    I'm still relatively confused.
     
  5. Mar 4, 2015 #4

    Dick

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    Let's set ##\sigma=\pi \alpha \pi^{-1}## for short. You've shown ##\sigma(\pi(\alpha_1))=\pi(\alpha_2)##. Generalizing that I'd say the cycle structure of ##\sigma## is ##(\pi(\alpha_1)\pi(\alpha_2)...)##. Still confused?
     
  6. Mar 4, 2015 #5
    Okay, that definitely makes its more clear. Thanks so much!
     
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