On the automorphism group of Fermat fields
type: Item
instance of: scholarly article
title: On the automorphism group of Fermat fields
zbMATH Open document ID: 0854.11062
author: Heinrich-Wolfgang Leopoldt
published in: Journal of Number Theory
publication date: 1997-01-19T00:00:00Z
review text: This paper was written in the early seventies and circulated among interested mathematicians. In the nineties the author gave his permission for publication. The manuscript has been read and arranged (where necessary) by H. Stichtenoth. The Fermat field of exponent \(n\) over the field \(\Omega\) is the field \(\Omega (x, y)\) with \(x^n+ y^n+ 1=0\). There are some obvious automorphisms of \(\Omega (x, y)/ \Omega\), which generate a group \(G_n\) called the Fermat group. The main result of the paper is the following theorem: Let \(n\geq 4\) and let \(\Omega\) be algebraically closed of any characteristic \(p\). If \(n-1\) is not a power of \(p\), then \(G_n\) is the full automorphism group of \(K_n/ \Omega\). If \(n- 1 =q\) is a power of \(p\) then \(PGU (3, q^2)\) is the full automorphism group of \(\Omega (x, y)/ \Omega\).
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 874179
zbMATH Keywords: Fermat field
zbMATH Keywords: Fermat group
zbMATH Keywords: automorphism group
reviewed by: Helmut Koch
MaRDI profile type: Publication
full work available at URL: jnth.1996.0017
OpenAlex ID: W2017699412
DOI: 10.1006/JNTH.1996.0017
description: scientific article; zbMATH DE number 874179