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Homework Help: Every odd permutation can be written

  1. Nov 29, 2007 #1
    1. The problem statement, all variables and given/known data
    If n>= 3 and S(n) is the symmetric group on n letters. prove every odd permutation in S(n) can be written as a product of 2n+3 transpositions, and every even permutation can be written as a product of 2n + 8 transpositions.


    2. Relevant equations



    3. The attempt at a solution

    Actually you know, i don't even understand the question. the previous parts say
    1) every permutation in S(n) can be written as a product of at most n-1 transpositions.
    2)every permutation in S(n) that is not a cycle can be written as a product of n-2 transpositions.

    So i'm assuming that you can just multiply any odd permutation by the identity enough times to reach 2n+3?
     
  2. jcsd
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