A prime decomposition symbol for a non-abelian central extension which is abelian over a bicyclic biquadratic field

Abstract

In a previous paper [6] we had some criteria for the prime decomposition in certain non-abelian extensions over the rational number fieldQ, and as its special case we had a reciprocity of the biquadratic residue symbol. The reciprocity was obtained by using a descent method of the prime decomposition for a central extension overQwhich is abelian over a biquadratic fieldIn the present paper we study on the case over a biquadratic fieldin general. We define a symbol [d1,d2,p] which expresses the decomposition law of a rational primepin a central extension mentioned above.