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Homework Help: What are the elements of Alt_4 ?

  1. Oct 17, 2007 #1

    quasar987

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    1. The problem statement, all variables and given/known data
    This is not HW per say, I'm just wondering what the elements of Alt_4 are (the subgroup of S4 consisting of all even permutations). I know Alt_4 is of order 4!/2=12, and I have so far that

    Id, (1 2 3), (1 2 4), (1 3 4), (2 3 4), (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)

    are in Alt_4 but what are the other four elements??
     
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  3. Oct 17, 2007 #2

    Dick

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    How about (1,3,2) for example?
     
  4. Oct 18, 2007 #3

    quasar987

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    Right, I forgot those.

    (1,3,2), (1 4 2), (1 4 3) and (2 4 3)

    the inverses of the four elements I listed.
     
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