Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Nilpotency Criterion for the Derived Subgroup of a Finite Group   It is proved that the derived subgroup of a finite group is nilpotent if and
only if $|ab|\ge |a||b|$ for all primary commutators $a$ and $b$ of coprime
orders.

35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin