Acyclicity for Groups and Vector Spaces

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.