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Math Help - Cycle Decomposition

  1. #1
    Super Member craig's Avatar
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    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?

    Thanks in advance
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  2. #2
    Super Member craig's Avatar
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    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?

    Thanks again in advance
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  3. #3
    Super Member craig's Avatar
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    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
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