# Homework Help: Every odd permutation can be written

1. Nov 29, 2007

### rsa58

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?