Write as a Product of Transpositions

[flufles]

Homework Statement

Write the permutation
P=
12345678
23156847

in cycle notation, and then write it as a product of transpositions

Homework Equations

The Attempt at a Solution

I got the cycle notation to be (123)(45687), but i am now not sure now to write it as a product of transpositions. My only really thought was just grouping the digits in twos but i don't think that is correct

Thank you

 

[I like Serena]

Welcome to PF, flufles!

Each cycle can be written as a product of transpositions.
The most common methods are:
(1 2 3 4) = (1 4)(1 3)(1 2)
and
(1 2 3 4) = (1 2)(2 3)(3 4).
See the pattern?

 

[flufles]

thank you for the welcome,
i think i do
so (123) could be written as (12)(23) or (13)(12)
and (45687) written as (45)(56)(68)(87) or (47)(48)(46)(45)
and so would i just put these next to each other as (12)(23)(45)(56)(68)(87)

Thank you

 

[I like Serena]

Yep! That's it!

And you're welcome.

 

[flufles]

thank you very much =]