Sectional rank and Cohomology

TL;DR

This paper establishes a bound on the first cohomology group's dimension for finite groups based on their sectional p-rank, linking group structure to cohomological properties.

Contribution

It introduces a new bound relating the first cohomology dimension to the sectional p-rank of finite groups, advancing understanding of their cohomological behavior.

Findings

Bound on first cohomology dimension in terms of sectional p-rank

Connection between group structure and cohomology

Applicable to absolutely irreducible modules in characteristic p

Abstract

We prove that there is a bound on the dimension of the first cohomology group of a finite group with coefficients in an absolutely irreducible in characteristic p in terms of the sectional p-rank of the group.