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 February 11th, 2017, 01:46 PM #1 Senior Member   Joined: Jan 2013 From: Italy Posts: 154 Thanks: 7 Permutation $(132)(45)$ as a product of transpositions. Hi, I have this permutation, expressed as product of transpositions: $\sigma = (132)(45) = (12)(13)(45) = (31)(32)(45)(12)(12)$ I understand that $(132)(45) = (12)(13)(45)$, is obtained keeping locked the $1$ in the first cycle and pairing it first with $2$ at the third position, and then with $3$ in the second position. Then, leaving intact $(45)$ since it is already a cycle of two elements. but, how to obtain $(31)(32)(45)(12)(12)$? Can you help me? Thanks!

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