Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A-nuclei and A-centers of a quasigroup   A-nuclei (groups of regular permutations) of a quasigroup are studied. A
quasigroup is A-nuclear if and only if it is group isotope. Any quasigroup with
permutation medial or paramedial identity is an abelian group isotope.
Definition of A-center of a quasigroup is given. A quasigroup is A-central if
and only if it is abelian group isotope. If a quasigroup is central in
Belyavskaya-Smith sense, then it is A-central. Conditions when A-nucleus define
normal congruence of a quasigroup are established, conditions normality of
nuclei of some inverse quasigroups are given. Notice, definition of A-nucleus
of a loop and A-center of a loop coincides, in fact, with corresponding
standard definition.

1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex