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
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
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