We were doing quotient groups in the Algebra class and we mentioned that if $N\unlhd G$ and $G$ abelian, then is $G/N$ also abelian. After that the professor gave the following example:
Symmetric group $S_n$ is not abelian for $n\geq 3$, but $S_n/A_n$ is abelian.
I don't understand why that is. Basically I'm supposed to see that for $\pi,\sigma \in S_n$ $\pi A_n \sigma A_n =\sigma A_n \pi A_n$, or equivalently $\pi \sigma A_n=\sigma\pi A_n$, but I can't. What am I missing?
Thanks in advance!