Generic extensions and generic polynomials for semidirect products

Abstract

This paper presents a generalization of a theorem of Saltman on the existence of generic extensions with group A G over an infinite field K , where A is abelian, using less restrictive requirements on A and G. The method is constructive, thereby allowing the explicit construction of generic polynomials for those groups, and it gives new bounds on the generic dimension. Generic polynomials for several small groups are constructed.