Consider the symmetric and alternating groups $S_n$ and $A_n$ ($n>2$).
1. Does arbitrary $2$-cycle and an arbitrary $n$-cycle in $S_n$ generates $S_n$?
2. If $n$ is odd, does an arbitrary $3$-cycle and arbitrary $n$-cycle in $S_n$ generates the subgroup $A_n$?
3. What are the references which give various "presentations" of $S_n$, $A_n$, and about order of products in $S_n$?.