Orbits of automorphism groups of fields

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We address several specific aspects of the following general question: can a field K have so many automorphisms that the action of the automorphism group on the elements of K has relatively few orbits? We prove that any field which has only finitely many orbits under its automorphism group is finite. We extend the techniques of that proof to approach a broader conjecture, which asks whether the automorphism group of one field over a subfield can have only finitely many orbits on the complement of the subfield. Finally, we apply similar methods to analyze the field of Mal'cev-Neumann "generalized power series" over a base field; these form near-counterexamples to our conjecture when the base field has characteristic zero, but often fall surprisingly far short in positive characteristic.
15 pages; v2: refereed version

Keywords

Commutative Algebra, Number Theory, 12F10 (Primary) 12J25 (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/72028

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0407473
 http://arxiv.org/abs/math/0407473

Collections

arXiv