How to Perform a Permutation with Multiple Cycles

[halvizo1031]

Homework Statement

(1 2) (1 4 5) (2 3 4) (2 5)= (1 4) (3 5)

Homework Equations

The Attempt at a Solution

Can someone explain to me how to do this permutation? I know it's the easiest thing to do but i just went blank! how did my professor get (1 4) (3 5)?

 

[lanedance]

start by writing out each step explicitly

eg for the permutation p = (25) you have
p(1) = 1
p(2) = 5
p(3) = 3
p(4) = 4
p(5) = 2

so this gives p as the following map
1 2 3 4 5
1 5 3 4 2

then similar for the next permutations, then either stack the maps or cualcte where each element ends up to get the effect of composition of several permutations and you should be able to read off the final result