A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is
Let ρ : G → GL(n, F) be a faithful representation of a finite group G and χ : G −→ F × a linear character. We study the module F[V ] G χ of χrelative invariants. We prove a modular analogue of result of R. P. Stanley and V. Reiner in the case of nonmodular reflection groups to the effect that these modules are free on a single generator over the ring of invariants F[V ] G . This result is then applied to show that the ring of invariants for H = ker(χ) ≤ G is Cohen-Macaulay. Since thedoi:10.1090/s0002-9939-06-08427-9 fatcat:xcyh7pfy7rebjlu2jrlb3yrpaa