The fundamental theorem of symmetric polynomials implies that the are algebraic independent, and thus that the map that sends each to the corresponding is a field isomorphism from to . This means that one may consider as a generic equation. This finishes the proof that the Galois group of a general equation is the symmetric group, and thus proves the original Abel–Ruffini theorem, which asserts that the general polynomial equation of degree cannot be solved in radicals for .
The fundamental theorem of symmetric polynomials implies that the are algebraic independent, and thus that the map that sends each to the corresponding is a field isomorphism from to  This means that one may consider as a generic equation. This finishes the proof that the Galois group of a gene.ral equation is the symmetric group, and thus proves the original Abel–Ruffini theorem, which asserts that the general polynomial equation of degree cannot be solved in radicals for .