Just a quick question. I've been asked to express $\displaystyle (1234)$ as a product of 3 transpositions with $\displaystyle (34)$ as the right hand factor.

Would $\displaystyle (43)(123)(34)$ a valid answer?

Thanks in advance

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- Mar 14th 2010, 02:19 PMcraigCycle Decomposition
Just a quick question. I've been asked to express $\displaystyle (1234)$ as a product of 3 transpositions with $\displaystyle (34)$ as the right hand factor.

Would $\displaystyle (43)(123)(34)$ a valid answer?

Thanks in advance - Mar 14th 2010, 02:33 PMcraig
Just remembered that the transposition $\displaystyle (ab) = (ba)$, so guess my next questions is how to answer this?

Earlier in the question I showed that $\displaystyle (1234)(34) = (abc)$ where $\displaystyle (abc) = (123)$.

Also deduced that $\displaystyle (1234) = (abc)(34)$ using the $\displaystyle (abc)$ from above.

Guessing I need to use this to answer the question, not sure how to start though?

Thanks again in advance - Mar 14th 2010, 02:40 PMcraig
Sorry I seem to have a habit of answering my own questions.

Though a little trial and error I've found that:

$\displaystyle (23)(13)(34) = (1234)$, could someone verify this?

Also is there a way I*should*have done this, ie. a more efficient way that trial and error?

Thanks again, and sorry for taking up all of the thread :)