Hyper-atoms applied to the critical pair Theory

TL;DR

This paper introduces hyper-atoms, a new concept that enhances the classical critical pair theory and improves key results like the Kemperman Structure Theorem.

Contribution

The paper presents the novel notion of hyper-atoms and demonstrates their application in strengthening fundamental theorems in critical pair theory.

Findings

Hyper-atoms are defined and their basic properties established.

The method improves existing results in critical pair theory.

Enhancements are made to the Kemperman Structure Theorem.

Abstract

We introduce the notion of a hyper-atom and prove a basic property of this object. This new method allows to improve several results in the classical critical pair theory including its cornerstone: the Kemperman Structure Theorem.