Orders of permutations

• Oct 16th 2008, 07:02 AM
universalsandbox
Orders of permutations
What is the order of a permutation telling you about it?
And how to find the following orders

(1 5 4)(2 3 7)(6 8)
(1 3 5 7)(2 6)(4 8)

Thanks!
• Oct 16th 2008, 08:54 AM
ThePerfectHacker
Quote:

Originally Posted by universalsandbox
What is the order of a permutation telling you about it?
And how to find the following orders

(1 5 4)(2 3 7)(6 8)
(1 3 5 7)(2 6)(4 8)

Thanks!

Since these are disjoint cycles the order is the lcm of their lengths.
• Oct 16th 2008, 03:31 PM
universalsandbox
so how would you find the length of a cycle?
• Oct 16th 2008, 06:12 PM
ThePerfectHacker
Quote:

Originally Posted by universalsandbox
so how would you find the length of a cycle?

The length of $\displaystyle (1 5 4)$ is $\displaystyle 3$.
The length of $\displaystyle (237)$ is $\displaystyle 3$.
The length of $\displaystyle (68)$ is $\displaystyle 2$.

Find $\displaystyle \text{lcm}(3,3,2) = 6$.
And that is the order.