Cycle Permutation: Composition of (12345)(12345)

[KevinL]

I feel like I'm doing this correctly but my professor gave us an answer that is different from what I'm getting.

Composition of (12345)(12345)

Reading right to left I get (13524) but the answer he gives is (135)(24)

The odd thing is I'm getting the rest of these correct so I don't feel like I'm doing it wrong.

 

[lanedance]

actually scratch that, made an error will get back to you

 

[lanedance]

so just to be clear on notation, as it can get tricky I read p=(123) as acting as follows
p(1)=2
p(2)=3
p(3)=1

so applying this to the 3 case gives
(123) 123
=231

and note
(123)=(231)=(312)

so applying this in your case
(12345) 12345
=23451
(12345) 23451
34512

so we have
12345
34512

which gives (13524), same as you

not applying (135)(24) gives
(135) 12345
=32541
(24) 32541
34521
which is not the same

sorry for the alignment, can't get it to work