Acyclicity for Groups and Vector Spaces

TL;DR

This paper introduces a duality of acyclic matching to classify Abelian groups and explores matchings in vector spaces, connecting group and vector space matchings using additive number theory, combinatorics, and algebra.

Contribution

It presents a new duality concept for acyclic matchings and links matchings in groups and vector spaces for classification purposes.

Findings

Acyclic matching duality for Abelian groups

Connection established between group and vector space matchings

Tools from additive number theory, combinatorics, and algebra used

Abstract

The notion of acyclic matching property was provided by Losonczy and it was proved that torsion-free groups admit this property. In this paper, we introduce a duality of acyclic matching as a tool for classification of some Abelian groups, moreover, we study matchings for vector spaces and give a connection between matchings in groups and vector spaces. Our tools mix additive number theory, combinatorics and algebra.