Abstract
IfVis a faithful module for a finite groupGover a field of characteristicp, then the ring of invariants need not be Cohen–Macaulay ifpdivides the order ofG. In this article the cohomology ofGis used to study the question of Cohen–Macaulayness of the invariant ring. One of the results is a classification of all groups for which the invariant ring with respect to the regular representation is Cohen–Macaulay. Moreover, it is proved that ifpdivides the order ofG, then the ring of vector invariants of sufficiently many copies ofVis not Cohen–Macaulay. A further result is that ifGis ap-group and the invariant ring is Cohen–Macaulay, thenGis a bireflection group, i.e., it is generated by elements which fix a subspace ofVof codimension at most 2.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
