Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On F-inverse covers of finite-above inverse monoids   Finite-above inverse monoids are a common generalization of finite inverse
monoids and Margolis--Meakin expansions of groups. Given a finite-above
$E$-unitary inverse monoid $M$ and a group variety $\mathit{U}$, we find a
condition for $M$ and $\mathit{U}$, involving a construction of descending
chains of graphs, which is equivalent to $M$ having an $F$-inverse cover via
$\mathit{U}$. In the special case where $\mathit{U}=\mathit{Ab}$, the variety
of Abelian groups, we apply this condition to get a simple sufficient condition
for $M$ to have no $F$-inverse cover via $\mathit{Ab}$, formulated by means of
the natural parial order and the least group congruence of $M$.

20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess