On local matching property in groups and vector space

TL;DR

This paper introduces the concept of locally matchable subsets in groups and their linear analogues in field extensions, providing new proofs and insights using additive number theory, combinatorics, and algebra.

Contribution

It defines local matching properties in groups and vector spaces, offering a novel approach and tools for matching theory and its linear analogue.

Findings

Introduction of local matching property in groups

Linear analogue for subspaces in field extensions

Alternative proofs for existing matching theory results

Abstract

In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue of local matching property for subspaces in a field extension. Our tools mix additive number theory, combinatorics and algebra.