1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted