Write as a single cycle or product of disjointed cycles and as a product of 2-cycles.
A) alph*beta where
alph=
1 2 3 4 5 6 7 8
2 3 4 5 1 7 8 6
beta=
1 2 3 4 5 6 7 8
1 3 8 7 6 5 2 4
I found that alph*beta=
1 2 3 4 5 6 7 8
2 4 6 8 7 1 3 5
but I dont know how to get the rest?
B)
(1 2 3)^-1 (2 3) (1 2 3)
right.
now, start the cylcle by starting with 1, so you write (1
now, follow where it leads until you get back to 1. that, see that 1-->2, 2-->4, 4-->8, 8 -->5, 5-->7, 7-->3, 3--> 6, 6 --> 1
so you have
(1 2 4 8 5 7 3 6)
and that's everybody. now, break it up into transpositions (2-cycles) and you can take it from there
note that