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Writing disjoint cycles

  1. Mar 26, 2016 #1

    RJLiberator

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    1. The problem statement, all variables and given/known data

    Screen Shot 2016-03-26 at 3.57.24 PM.png
    2. Relevant equations


    3. The attempt at a solution


    My answers for the disjoint cycles of f,g,h,k are as follows. My question concerns my disjoint cycles for g. Are we allowed to have 3 cycles? I would think "yes" because that just makes sense to me.

    for f: ( 1 3 8 4 6) (2 5)
    g: (2 6 7) (3 8) (4 5)
    h: (1 8 7 3 5 2) (4 6)
    k: (1 5 4) (2 3 8)

    For orders:

    order f: lcm(5, 2) = 10
    order g: lcm ( 3, 2) = 6
    order h: lcm(6, 2) = 6
    order k: lcm(3, 3) = 3
     
    Last edited: Mar 26, 2016
  2. jcsd
  3. Mar 26, 2016 #2

    RJLiberator

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    Also, if I wanted to write f as a product of transpositions I would take:
    f = (1 3 8 4 6) (2 5)
    product of transpositions: (1,3)(3,8)(8,4)(4,6)(2,5)
    5 total so odd permutation
     
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