The finiteness theorem for invariants of a finite group (translation of Emmy Noether's "Der Endlichkeitsatz der Invarianten endlicher Gruppen")

TL;DR

This paper provides an elementary proof that the invariants of a finite group are finitely generated, offering a constructive approach using symmetric functions, contrasting with the traditional Hilbert basis theorem proof.

Contribution

It presents a simple, elementary proof of the finiteness of invariants for finite groups, providing explicit invariants rather than just an existence proof.

Findings

Elementary finiteness proof using symmetric functions

Explicit construction of a complete system of invariants

Contrasts with the Hilbert basis theorem approach

Abstract

A translation of Emmy Noether's paper "Der Endlichkeitsatz der Invarianten endlicher Gruppen" (Mathematische Annalen, vol. 77, 1920, pages 89--92). In Noether's words, the paper gives "an entirely elementary finiteness proof---using only the theory of symmetric functions---for the invariants of a finite group, which at once supplies an actual statement of a complete system of invariants while the usual proof using the Hilbert basis theorem is only an existence proof."