Descent cohomology and factorizations of groups

TL;DR

This paper classifies group factorizations using descent cohomology, extending Serre's non-abelian cohomology to monoids, providing a unified framework for understanding group structures.

Contribution

It introduces a full classification of group factorizations via descent cohomology, generalizing Serre's non-abelian cohomology to monoids.

Findings

Descent cohomology encompasses Serre's non-abelian cohomology.

Provides a complete classification of group factorizations.

Extends cohomology theory to include monoids.

Abstract

The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special case. This enables us to generalize Serre's theory further to include monoids.