A new proof for the Erd\H{o}s-Ko-Rado Theorem for the alternating group

A subset $S$ of the alternating group on $n$ points is {\it intersecting} if for any pair of permutations $\pi ,\sigma$ in $S$, there is an element $i\in {1,\dots,n}$suchthat$\pi(i)=\sigma(i)$\mathrm{.}Weprovethatif$S$ is intersecting, then $\mathrm{\mid }S\mathrm{\mid }\le \frac{(n-1)!}{2}$. Also, we prove that if $n \geq 5$,thentheonlysets$S$ that meet this bound are the cosets of the stabilizer of a point of $\{1,\dots ,n\}$.