On local matchability in groups and vector spaces
  In this paper, we define locally matchable subsets of a group which is extracted 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 locally matchability for subspaces in a field extension. Our tools mix additive number theory, combinatorics and algebra 
Mohsen Aliabadia, Mano Vikash Janardhanan
math.GR math.CO