The computation of the cohomology rings of all groups of order 128

TL;DR

This paper computes the mod-2 cohomology rings for all groups of order 128, confirming Benson's Regularity Conjecture for groups of order less than 256, thus advancing understanding of their algebraic properties.

Contribution

It provides the first complete computation of cohomology rings for all groups of order 128, a significant extension in group cohomology research.

Findings

All groups of order less than 256 satisfy Benson's Regularity Conjecture

Complete classification of cohomology rings for 2328 groups of order 128

Supports conjecture validity across a broader class of groups

Abstract

We describe the computation of the mod-2 cohomology rings of all 2328 groups of order 128. One consequence is that all groups of order less than 256 satisfy the strong form of Benson's Regularity Conjecture.