Alternating group (awaiting review)

The alternating group, denoted $A_n$ is the subgroup of the symmetric group consisting of the even permutations. For $n\ge2$ it is of order $\frac{n!}{2}$, and is index $2$ in $S_n$. The group is solvable for $n\leq 4$ and simple for $n\geq 5$.