Generic Extensions and Generic Polynomials

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. Key words: Constructive Galois theory, Kummer theory, Generic polynomials, Semidirect products

• Type: Journal
• Year: 2000
• Where: JSC
• Authors: Arne Ledet
• Keywords: Generic Dimension, Generic Extensions, Generic Polynomials, JSC 2000