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The order of a permutation cycle 
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#1
Sep807, 04:20 PM

P: 569

1. The problem statement, all variables and given/known data
what is the order of kcycle (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.(Ruffini1799) in this case , the length of the kcycle 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
Sep807, 05:05 PM

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Thanks
P: 25,251

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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