Testing Benson's Regularity Conjecture

TL;DR

This paper verifies Benson's conjecture that group cohomology rings have a special regularity property, confirming it for all groups of order less than 256 through computational methods.

Contribution

It provides computational evidence supporting Benson's conjecture for all groups of order under 256, extending the known cases.

Findings

Conjecture holds for groups of order less than 256

Supports the idea that cohomology rings have special regularity properties

Computational methods are effective for testing algebraic conjectures

Abstract

D. J. Benson conjectures that the Castelnuovo-Mumford regularity of a group cohomology ring is always zero. More generally he conjectures that the cohomology ring always has a system of parameters satisfying a property he calls very strong quasi-regular. Using computer calculations we find that the more general conjecture holds for all groups of order less than 256.