The cohomology rings of rank 3 simple groups are Cohen-Macaulay

TL;DR

This paper proves that the mod 2 cohomology rings of all finite simple groups of rank 3 or less are Cohen-Macaulay, revealing a significant algebraic property of these groups.

Contribution

It establishes the Cohen-Macaulay property for the mod 2 cohomology rings of finite simple groups of rank at most 3, a previously unknown structural result.

Findings

All finite simple groups of rank ≤ 3 have Cohen-Macaulay mod 2 cohomology rings.

The result applies to groups at the prime 2, highlighting a uniform algebraic property.

This advances understanding of the cohomological structure of finite simple groups.

Abstract

In this paper we show that the mod 2 cohomology ring of any finite simple group of rank 3 or less (at the prime 2) must be Cohen-Macaulay.