Automorphisms of congruence function fields
type: Item
instance of: scholarly article
title: Automorphisms of congruence function fields
zbMATH Open document ID: 0694.12011
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \(k\) be a finite field. For a function field \(K\) over \(k\) and \(m\geq 3\), it is proven that there are infinitely many non-isomorphic function fields \(L\) such that \(L/K\) is a separable extension of degree \(m\) and \(Aut_k L=\{\text{Id}\}\). It is also shown that for a finite group \(G\), there are infinitely many non-isomorphic function fields \(L/k\) such that \(Aut_k L\cong G\). Finally, given any finite nilpotent group \(G\) such that \(| G| >1\) and (\(| G|, | k| -1)=1\), and any function field \(K\) over \(k\), there are infinitely many non-isomorphic function fields \(L\) over \(k\) with \(\mathrm{Gal}(L/K) = \Aut_k L\cong G\).
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 4136072
zbMATH Keywords: congruence function fields
zbMATH Keywords: automorphism groups
author: Martha Rzedowski-Calderón
author: Gabriel D. Villa Salvador
MaRDI profile type: Publication
full work available at URL: pjm.1991.150.167
OpenAlex ID: W2035980325
DOI: 10.2140/PJM.1991.150.167
description: scientific article; zbMATH DE number 4136072