# Order of premutation

• Aug 6th 2007, 09:25 PM
r7iris
Order of premutation
Compute the orders of products of non-disjoint cycles:

(1 2 3)(3 2 4)

(1 2 3)(3 4 5)

I calcuated for a couple of times but still couldn't get the right answers.
• Aug 7th 2007, 05:22 AM
ThePerfectHacker
Quote:

Originally Posted by r7iris
Compute the orders of products of non-disjoint cycles:

(1 2 3)(3 2 4)

(1 2 3)(3 4 5)

I calcuated for a couple of times but still couldn't get the right answers.

What is the permutation group you are working in? Is it $\displaystyle S_5$?
• Aug 7th 2007, 10:33 AM
r7iris
They are two separate questions.
• Aug 7th 2007, 12:01 PM
topsquark
(Grumbles) I never was good with cyclic notation. :o

-Dan
• Aug 7th 2007, 01:05 PM
ThePerfectHacker
Just write it as a premutation,

$\displaystyle \tau = \left( \begin{array}{cccc}1&2&3&4 \\ 2&4&3&1 \end{array} \right)$

Now find $\displaystyle \tau , \tau^2 , ...$
Until you find,
$\displaystyle \tau^n = \left( \begin{array}{cccc}1&2&3&4 \\ 1&2&3&4 \end{array} \right)$