I know that if I have any permutation, this permutation can be written as the product of transpositions. Now the number of these transpositions may be odd or even depending on my permutation. I also know that any transposition can be written as the product of simple transpositions (the pair $(i,i+1)$). So this means that any permutation can be written as the product of simple transpositions and the number of these transpositions may be odd or even depending on the permutation. Have I missed anything?
Odd or Even number of transpositions
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abstract-algebra
group-theory
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0Please help me. Tha$n$k you. http://math.stackexchange.com/questions/423297/how-to-explain-that-1-32-4-1-3-2-4 – 2013-06-18
1 Answers
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No, you have not missed anything. But you should probably state explicitly that no permutation can be written both as an even number of transpositions and an odd number of transpositions.