Generic extensions and generic polynomials for semidirect products

This paper presents a generalization of a theorem of Saltman oil the existence of generic extensions with group A x G over ail infinite field K, where A is abelian, using less restrictive requirements oil A and G. The method is constructive, thereby allowing the explicit construction of generic polynomials for those groups, and it gives new bounds oil the generic dimension. Generic polynomials for several small groups are constructed. (C) 2009 Elsevier Inc. All rights reserved.