Neocities.org

>the_quintic_problem Therefore an equation of degree n has general solutions if and only if Sn is solvable. And since Sn is a finite group, it means whether Sn has a composition series in which all factor groups are Zp. This corresponds to that by adding the primitive p-th root of unity, you can extend the base field to the field that factorizes the polynomial. But for n>4, An is simple so that Sn is not solvable.