Question

Express as a product of disjoint cycles: (1,4,2,3,5)(1,3,4,5).

Answer 1

yay! permuatations

Answer 2

i believe we do this from right to left ...

first write out the ... numbers

1 2 3 4 5 , cycle 1>3>4>5>1
3 4 5 1 , then cycle 1>4>2>3>5>1
5 3 2 1 4

Answer 3

soo, the simplified form is:

1 2 3 4 5
5 3 2 1 4

1>5>4>1 and 2>3>2

(1,5,4)(2,3) is the product of cycles for it

Answer 4

does the order matter because I had (5,4,1)(3,2)

Answer 5

order shouldnt matter as long as they are equivalent cycles

Answer 6

(1,5,4) ~ (5,4,1) ~ (4,1,5)