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.

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- Aug 6th 2007, 09:25 PMr7irisOrder 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 AMThePerfectHacker
- Aug 7th 2007, 10:33 AMr7iris
They are two separate questions.

- Aug 7th 2007, 12:01 PMtopsquark
(Grumbles) I never was good with cyclic notation. :o

-Dan - Aug 7th 2007, 01:05 PMThePerfectHacker
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,

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