My Math Forum Transposition of Permutation Check my Work Please

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 September 26th, 2010, 10:44 PM #1 Newbie   Joined: Sep 2010 Posts: 22 Thanks: 0 Transposition of Permutation Check my Work Please I understand that if we have $(12345)$ that it has many ways to transpose it and one way is $(15)(14)(13)(12)$ and that makes it even since there are four of them. What if it asks me to transpose $\pi = \left(\begin{array}{llllllll} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 7 & 4 & 1 & 5 & 6 & 2 & 3 & 8 \\ \end{array}\right)$. Would I just do the product of disjoint cycles and then transpose it? I tried that and here is what I got: Product of disjoint cycles is $\pi= (173)(2456)(731)$ and the transpose $\pi= (13)(17)(26)(25)(24)(71)(73)$ which is odd. Is this correct?

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