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The order of a permutation cycle

by Benzoate
Tags: cycle, order, permutation
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Sep8-07, 04:20 PM
P: 569
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?
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Sep8-07, 05:05 PM
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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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