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The order of a permutation cycle

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data

    what is the order of k-cycle (a(1),a(2),...,a(k))

    2. Relevant equations

    3. The attempt at a solution

    According to the theorem of the order of a permutation: the order of a permutation set written in disjoint cycle form is the least common multiple of the lengths of the cycles.(Ruffini-1799)

    in this case , the length of the k-cycle is k, for all the common multiples of a(1), a(2) ... and a(k) would be k. So the order of cycle k is k right?
  2. jcsd
  3. Sep 8, 2007 #2


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    The length of the cycle is k so the order is k. It doesn't matter what a(1) etc are. If I understand your notation.
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