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Permutation orders

  1. Jan 18, 2009 #1
    I am sure this is very simple but I m kind of confused here.

    What is this product equal to and what's the order of the permutation?

    (1 2 3 4 5 6 7) (3 6 7 4 2 5 1)

    I thought it was (3 7 5 2 6 1 4) but I am reading somewhere that it should be (137)(265)(4) and hence has order 3.

    Why is this "(3 7 5 2 6 1 4)" not correct? I mean I thought I had to start with the last cycle and do 3-->6, in the first cycle, 6-->7
    and then 7-->4, in the first cycle, 4-->5,...

    So I would get something like (3 7 5 ...

    I am very confused here, help :))
     
  2. jcsd
  3. Jan 18, 2009 #2

    Dick

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    That isn't cycle notation. Are you sure they didn't write this on two rows, like
    (1 2 3 4 5 6 7)
    (3 6 7 4 2 5 1)
    The first row is just the argument of the permutation and the second row is it's value.
    I.e. 1->3 2->6 3->7 4->4 5->2 6->5 7->1
     
    Last edited: Jan 18, 2009
  4. Jan 18, 2009 #3
    Oh I see, so if it was a product of cycles, my answer would have been correct and the order of the product would be 7. But in this case, we just have the argument of a permutation and its value. So the question here is not to find the order of the product of two cycles but rather the order of the single permutation (given the argument and the value).
    Is that correct?
     
  5. Jan 18, 2009 #4

    Dick

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    It looks like that to me. It seems to fit with the given answer.
     
  6. Jan 18, 2009 #5
    thanks.
     
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