Nonvanishing cohomology classes on finite groups of Lie type with Coxeter number at most p

TL;DR

This paper proves that certain cohomology groups of finite groups of Lie type are nonzero under specific conditions, using an explicit construction, advancing understanding of their algebraic structure.

Contribution

It establishes nonvanishing of cohomology for finite Lie type groups with Coxeter number at most p, providing a simple explicit construction of a nonzero element.

Findings

Cohomology in degree r(2p-3) is nonzero for these groups.

Explicit construction of a nonzero cohomology class.

Results apply to groups with Coxeter number ≤ p.

Abstract

We prove that the degree $r(2p-3)$ cohomology of any finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a simple explicit construction of a nonzero element.