DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

Article in press

Authors:

Mohsen Aliabadi Aliabadi

Mohsen Aliabadi

University of California, San Diego

email: mohsenmath88@gmail.com

Title:

Conditions for matchability in groups and field extensions II

PDF

Source:

Discussiones Mathematicae - General Algebra and Applications

Received: 2023-11-13 , Revised: 2024-04-06 , Accepted: 2024-04-07 , Available online: 2024-08-23 , https://doi.org/10.7151/dmgaa.1461

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

Keywords:

matching property

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