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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1So what exactly is your question? – 2011-03-22
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0that my statement is correct or not? – 2011-03-22
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0No, you haven't missed anything, and yes, your statement is correct :-) – 2011-03-22
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0You may have a look here: http://en.wikipedia.org/wiki/Parity_of_a_permutation – 2011-03-22
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0Please help me. Thank you. http://math.stackexchange.com/questions/423297/how-to-explain-that-1-32-4-1-3-2-4 – 2013-06-18