Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Buchsteiner loops: associators and constructions   Let $Q$ be a Buchsteiner loop. We describe the associator calculus in three
variables, and show that $|Q| \ge 32$ if $Q$ is not conjugacy closed. We also
show that $|Q| \ge 64$ if there exists $x \in Q$ such that $x^2$ is not in the
nucleus of $Q$. Furthermore, we describe a general construction that yields all
proper Buchsteiner loops of order 32. Finally, we produce a Buchsteiner loop of
order 128 that is nilpotency class 3 and possesses an abelian inner mapping
group.

12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an