Conditions for matchability in groups and vector spaces II

Abstract

We present sufficient conditions for the existence of matchings in abelian groups and their linear counterparts. These conditions lead to extensions of existing results in matching theory. Additionally, we classify subsets within abelian groups that cannot be matched. We introduce the concept of Chowla subspaces and formulate and conjecture a linear analogue of a result originally attributed to Y. O. Hamidoune [20] concerning Chowla sets. If proven true, this result would extend matchings in primitive subspaces. Throughout the paper, we emphasize the analogy between matchings in abelian groups and field extensions. We also pose numerous open questions for future research. Our approach relies on classical theorems in group theory, additive number theory and linear algebra. As the title of the paper suggests, this work is the second sequel to a previous paper [5] with a similar theme. This paper is self-contained and can be read independently.Comment: Comments are welcom