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I'm stuck on a homework problem that asks

Write the cycle $(2 3 4)$ as a product of transpositions in $\{(1 2),(1 3), (1 4)\}$

I'm fine with computing permutations, but I don't know what the problem is asking. Specifically, what does the last part of the question imply?

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    I am very glad if you can help me on this. Thank you. http://math.stackexchange.com/questions/423297/how-to-explain-that-1-32-4-1-3-2-42013-06-18

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We want 2 to go to 3, 3 to go to 4, and 4 to go to 2 (while 1 goes nowhere).

Consider $(12)(13)$. 2 goes to 3, which is good, but 3 goes to 1, which is bad.

So consider $(12)(13)(14)$. Now 2 still goes to 3, and 3 now goes to 4, which is good, but 4 goes to 1, which is bad.

So consider $(12)(13)(14)(12)$.

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    Yes. I've been taught using the right-to-left method, so (12)(14)(13)(12) for me. Thanks for the explanation!2011-12-07