E. Noether's bound in the invariant theory of finite groups
type: Item
instance of: scholarly article
title: E. Noether's bound in the invariant theory of finite groups
zbMATH Open document ID: 0854.13006
DOI: 10.1007/BF01273338
author: Larry Smith
published in: Archiv der Mathematik
publication date: 1997-01-06T00:00:00Z
review text: Let \(\rho:G\hookrightarrow\text{GL}(n,\mathbb{F})\) be a faithful representation of the finite group \(G\) over the field \(\mathbb{F}\). In 1916, \textit{E. Noether} proved that for \(\mathbb{F}\) of characteristic zero the ring of invariants \(\mathbb{F}[ V]^G\) is generated as an algebra by the invariant polynomials of degree at most \(|G|\). It is known that Noether's bound on the degrees of the generators of \(\mathbb{F}[ V]^G\) holds more generally when the characteristic of \(\mathbb{F}\) is greater than \(|G|\). In this note we prove that Noether's bound holds when \(G\) is solvable and \(|G|\) is relatively prime to the characteristic of \(\mathbb{F}\).
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 937052
zbMATH Keywords: ring of invariants
zbMATH Keywords: invariant polynomials
MaRDI profile type: Publication
cites work: Solvability of groups of odd order
cites work: Q4838154
cites work: Q4435456
description: scientific article; zbMATH DE number 937052