# Cycle Decomposition

• Mar 14th 2010, 03:19 PM
craig
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?

• Mar 14th 2010, 03:33 PM
craig
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?

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