Abstract.
We prove the following result: If G is a finite irreducible reflection group defined over a base field k, then the invariant field of G is purely transcendental over k, even if |G| is divisible by the characteristic of k. It is well known that in the above situation the invariant ring is in general not a polynomial ring. So the question whether at least the invariant field is purely transcendental (Noether's problem) is quite natural.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 14 January 1998
Rights and permissions
About this article
Cite this article
Kemper, G., Malle, G. Invariant fields of finite irreducible reflection groups. Math Ann 315, 569–586 (1999). https://doi.org/10.1007/s002080050329
Issue Date:
DOI: https://doi.org/10.1007/s002080050329