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Abstract Algebra matrix

  1. Dec 26, 2011 #1
    Write the following in two row matrix form.


    (1874)(36759)



    I have

    [1 2 3 4 5 6 7 8 9]
    [8 2 6 1 9 7 4 7 3]

    my problem is couldnt 7 also go to 5 and have 8 going to 7 and 6 going to 7 so Im sure I am wrong but I am not sure why.
     
  2. jcsd
  3. Dec 26, 2011 #2

    micromass

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    With (1874)(36759) they mean the COMPOSITION of two permutation. So you first need to apply (36759) and then (1874). So you first need to work out the composition before you write down the matrix.
     
  4. Dec 26, 2011 #3
    oh that would make more sense. So how would I go about doing that.

    would I say that
    3->6
    6->7
    5->9
    9->3

    then
    1->8
    8->7
    7->4
    4->1

    and since 6->7 and 7-> 4 I can say 6->4

    [1 2 3 4 5 6 7 8 9]
    [8 2 6 1 9 4 ? 7 3] and since 5 hasnt been used would I just stick it in to get 7->5


    [1 2 3 4 5 6 7 8 9]
    [8 2 6 1 9 4 5 7 3]

    Is that right?
     
  5. Dec 26, 2011 #4

    micromass

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    You forgot to put 7->5 here. You can read that off (1874)(36759)

    Yes.
     
  6. Dec 26, 2011 #5
    oops...... Thank you.
     
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