On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Gow, Rod, McGuire, Gary
Format: Preprint
Published: 2021
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909386869309440
author Gow, Rod
McGuire, Gary
author_facet Gow, Rod
McGuire, Gary
contents Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups.
format Preprint
id arxiv_https___arxiv_org_abs_2109_06693
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields
Gow, Rod
McGuire, Gary
Number Theory
Algebraic Geometry
Group Theory
12F12, 11S20
Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups.
title On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields
topic Number Theory
Algebraic Geometry
Group Theory
12F12, 11S20
url https://arxiv.org/abs/2109.06693