Permutations

[duki]

1. The problem statement, all variables and given/known data

Represent the following products as products of disjoint cycle. find the order of each product.

2. Relevant equations

a) (1234)(567)(261)(47)
b) (12345)(67)(1357)(163)
c) (14)(123)(45)(14)

3. The attempt at a solution

I've only attempted a) because I'm not sure if I'm doing it right. Here's what I got:

a) (163742)(5164)

because,
1->2, 2->6
2->3 so no need to include it
3->4, 4->7
4->1, 1->2
5->6, 6->1
6->7, 7->4
Is this even close?

[lanedance]

(1234) on the set should look like
|1-2-3-4|
|2-1-3-4| position 1->2
|2-3-1-4| position 2->3
|2-3-4-1| position 3->4

so (1234) is the permutation
|1-2-3-4|
|2-3-4-1|