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S(n) is not abelian

  1. Apr 12, 2005 #1
    I'm having troubles with this problem here -

    Show [tex]S_N[/tex] is not abelian for any [tex] n >= 3[/tex]

    now right now, im simply lost, of course its late at night so that might be why, so if some help could be provided that would be appreciated, also i would like it if you didnt simply give the proof, but also explained it.
     
  2. jcsd
  3. Apr 12, 2005 #2

    Hurkyl

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    Experiment. :smile: Start with S_3 and try to find two permutations that don't commute. Then, try S_4. Look for a pattern you can exploit.
     
  4. Apr 13, 2005 #3
    eh. Once you've done S3, you're done, since Sn contains S3 as a subgroup.
     
  5. Apr 13, 2005 #4

    Hurkyl

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    Yep. I'm hoping TsunamiJoe will notice that his example for S_3 will work for S_4 and all the others. :smile:
     
  6. Apr 13, 2005 #5
    |~|will respond with answer tomarow, was stupid and left textbook at school|~|
     
  7. Apr 13, 2005 #6

    Hurkyl

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    Do you need your textbook for this? You just need to know what kind of elements are in S_N and what abelian means.
     
  8. Apr 18, 2005 #7
    |~| that was not the only exercise to work on, and i try to keep a train of thought when doing maths like these |~|
     
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