Classifying abelian groups through acyclic matchings

The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E. K. Wakeford in 10. This linear algebra problem prompted C. K. Fan and J. Losonczy to introduce the notion of acyclic matchings in the additive group Zⁿ in 5, subsequently extended to abelian groups by the latter author9. Alon et al. , in 4, established the acyclic matching property for Zⁿ. This note aims to classify all abelian groups with respect to the acyclic matching property.