# Order of a Permutation

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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.

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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.