On the deduction of the class field theory from the general reciprocity of power residues (Q2709969)

The authors investigate the question whether the reciprocity of Artin for general abelian extensions of algebraic number fields can be elementarily deduced or not from the reciprocity of the power residue symbol concerning fields containing enough roots of unity. The answer is yes if the degree of the field extension is odd. If, however, the degree is even, it is likely that some more advanced tool is required for the purpose of deducing Artin's reciprocity law, for instance, Hasse's norm theorem for quadratic extension.