I am trying to write out what is in $A_4$ and $A_6$, their general form, not the whole $n!/2$ cause that would be a lot. My main question is how do I do that. I know they are all the even permutations from their symmetric groups respectively. I also know the identity is in each one of them.
Would this be it?
$A_4$: e, (abc), (ab)(cd)?
$A_6$: e, (abc), (abcde), (ab)(cd), (abcd)(ef), (abc)(def)?
Is this the write way to write it out?
Edit 1: If this is it, then why would I be asked to write $A_4$ as 8 three-cycles and 3 two-cycles?