The order of a permutation cycle

[Benzoate]

Homework Statement

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

Homework Equations

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?

 

[Dick]

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.