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Permutation as a Product of Transposition

  1. Sep 8, 2010 #1
    hi guys.. can you help me prove this theorem?
    Every permutation S_n where n>1 is a product of 2 cycles..
    i got a little confused with some books' proof..thnx
     
  2. jcsd
  3. Sep 8, 2010 #2
    Can you show some work you've done on this?

    The proof that comes to mind for me is to write each permutation as a product of cycles (you know how to do this, right?), and then you can explicitly describe how each cycle is a product of transpositions. For example, (1234) = (14)(13)(12).
     
  4. Sep 16, 2010 #3
    Yes, the thing that i don't understand is how the formula was derived. this is the formula
    (a_1, a_k) (a_1, a_k-1) ... (a_1, a_2).
     
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