1. ## Cycle Decomposition

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

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

2. Just remembered that the transposition $(ab) = (ba)$, so guess my next questions is how to answer this?

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

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

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

3. Sorry I seem to have a habit of answering my own questions.

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

$(23)(13)(34) = (1234)$, 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