RÉDEI FIELDS AND DYADIC EXTENSIONS

Abstract

For an arbitrary non-square discriminant D, the Rédei fieldΓ0(D) is introduced as an extension of [Formula: see text] analogous to the genus field and connected with the Rédei–Reichardt Theorem. It is shown how to compute Rédei fields, and this is used to find socles of dyadic extensions of K for negative D. Finally, a theorem and two conjectures are presented relating the fields [Formula: see text] and [Formula: see text] for an odd prime p.