Symmetric group $\left|\prod_{1\le i
I would like a hint and only a hint to prove
$\forall \sigma\in S_n$ , $S_n$ is a finite symmetric group of permutation
$\displaystyle \left|\prod\limits_{1\le i<j\le n}\big(\sigma(i)-\sigma(j)\big)\right|=\left|\prod\limits_{1\le i<j\le n}\big(i-j\big)\right|$
thanks !!

HINT: try by induction, starting from $n=2$
