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Homework Help: Cycle decomposition of n-cycle's power

  1. Nov 15, 2008 #1
    1. The problem statement, all variables and given/known data
    let a=(b_1,...,b_n) n-cycle in the permutation group S_n .
    prove that the cycle decomposition of a^k consist of gcd(n,k) cycles of n/gcd(n,k) size.

    3. The attempt at a solution
    I know that [tex]a^k(b_i)=b_{i+k (mod n)}[/tex]
    how can it help me ?
  2. jcsd
  3. Nov 16, 2008 #2


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    Science Advisor
    Homework Helper

    Have you tried playing with small examples and looking for patters than you can generalize?
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