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So I'm having a hard time with computations w/ cycles. Products, inverses, and orders.

  1. Oct 30, 2014 #1
    So I've been sitting here for a while looking at my study guide and I am not sure how to find the product (or even the inverse) of this permutation in S9:

    (2 5 1 3 6 4) (8 5 6)(1 9) = (1 3 8 5 9)(2 6 4) (Correct answer)

    I know it starts off with 1 --> 3, then you get (1 3 and then after you continue with 3 --> 6 --> 8. After you start with 6 --> 4, right? But I keep coming across the wrong answer. I get (1 3 8 4 2) (8 1)

    I'm pretty confused on this topic. If you could shed some light I'd greatly appreciate it. Thanks!
     
  2. jcsd
  3. Oct 30, 2014 #2

    Erland

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    Well, it was a long time ago I did those things, but, assuming that the permutations should be performed from left to right, I get:

    1 --> 3 --> 3 --> 3
    3 --> 6 --> 8 --> 8
    8 --> 8 --> 5 --> 5
    5 --> 1 --> 1 --> 9
    9 --> 9 --> 9 --> 1

    leading to the cycle (1 3 8 5 9)

    2 --> 5 --> 6 --> 6
    6 --> 4 --> 4 --> 4
    4 --> 2 --> 2 --> 2

    leading to the cycle (2 6 4)

    7 --> 7 --> 7 --> 7

    leading to the cycle (7)

    So, the answer is (1 3 5 8 9)(2 6 4)(7)

    but (7) needs perhaps not be included, or maybe the elements to be permuted don't even include 7. In any case, the book's answer is correct.
     
  4. Oct 30, 2014 #3


    Thanks a lot! Now it makes sense. Do you know how to find the inverse?
     
  5. Oct 30, 2014 #4

    Erland

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    Just go backwards!
     
  6. Oct 30, 2014 #5

    HallsofIvy

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    The convention that I am familiar with is that if a character is not changed by a permutation, it doesn't need to be mentioned.
    So your (1 3 5 8 9)(2 6 4)(7) can be written as (1 3 5 8 9)(2 6 4).
     
  7. Oct 31, 2014 #6
    Thanks guys! On the inverse problem as well. Appreciate it.
     
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