Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditions for matchability in groups and field extensions   The origins of the notion of matchings in groups spawn from a linear algebra
problem proposed by E. K. Wakeford [24] which was tackled in 1996 [10]. In this
paper, we first discuss unmatchable subsets in abelian groups. Then we
formulate and prove linear analogues of results concerning matchings, along
with a conjecture that, if true, would extend the primitive subspace theorem.
We discuss the dimension $m$-intersection property for vector spaces and its
connection to matching subspaces in a field extension, and we prove the linear
version of an intersection property result of certain subsets of a given set.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int