I'm sitting with an exercise I can't quite finish.
Let be defined as follows: (of course it's not actually a fraction, I just dont know how to write a permutation.)
I have already answered the first three exercises:
(a) - Write as a product of disjoint cycles : .
(b) - Determine and the order of : and so the order of is 4.
(c) - How many simple transpositions are needed to write as a product of simple transpositions : From (b) I had that and that is the number of simple transitions needed.
The exercise I can't quite figure out is this:
(d) - Find , the alternating group, so .
Could someone give me a tip on how to solve this? Thanks on beforehand.