# Product Permutations/cycle notation

1. Jul 7, 2011

### wontonsoup

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

This is just an example in a textbook but I'm completely stumped.
This is dealing with cycles, and product permutations.
So we have
p=(341)(52)
q = (1452)

and we want to compute the product permutation qp

2. Relevant equations

so qp = (1452) * (341)(25)

The book writes p sends 3 to 4 and q sends 4 to 5 so qp sends 3 to 5.

3. The attempt at a solution

I know that we proceed from right to left on the permutations, and go from left to right inside the cycles.

I realise that in a cycle, say (341) 3 -> 4-> 1-> 3.

Then in this problem of finding "qp" we start with 1, and the right-most permutation. Then from there I am lost. I suppose 1 -> 3 -> ?. after 1 sends to 3 in p, do we then find what 3 would send to in q (except there is no 3 in q)?The answer for this example is (135) but im completely lost on how to proceed. The book unfortunately isn't very clear on this. Could anybody give me some pointers on how to proceed? Thanks!

2. Jul 7, 2011

### tiny-tim

welcome to pf!

hi wontonsoup! welcome to pf!
(135) means that qp sends 1 to 3, qp sends 3 to 5, qp sends 5 to 1

qp sends 1 to 3 because (341) sends 1 to 3, and (1452) leaves 3 alone

qp sends 3 to 5 because (341) sends 3 to 4, and (1452) sends 4 to 5

qp sends 5 to 1 because (25) sends 5 to 2, and (1452) sends 2 to 1