# Order of a Permutation

Please see the attached file for the fully formatted problems.

Find the order of sigma^1000, where sigma is the permutation (123456789)

(378945216)

Find the order of , where is the permutation .

Solution. Since and . Let , we have

where k, m and n are positive integers.

So,

So, the order of is 3.

I got this solution but I don't understand why the permutation raised to the 1000 power=(138). Why do the other elements just map to themselves? Can you elaborate on this anymore. Also why is it necessary to put 1000= 333*3+1 = 500 * 2 = 250 * 4.

Â© BrainMass Inc. brainmass.com October 6, 2022, 10:48 am ad1c9bdddfhttps://brainmass.com/math/combinatorics/order-permutation-11928

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Find the order of , where is the permutation .

Solution. Since and . Let , we have

where k, m and n are positive integers.

So,

So, the order of is 3.

I got this solution but I don't understand why the permutation raised to the 1000 ...

#### Solution Summary

The order of a permutation is found. The solution is detailed and well presented.