Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On finite $p$-groups satisfying given laws   A variety of groups does not contain all metabelian groups if and only if
there is an absolute bound for the nilpotency classes of powerful $p$-groups in
the given variety. Similarly, a variety contains only finitely many finite
$p$-groups of any given coclass if and only if not every group that is an
extension of an abelian group by an elementary abelian $p$-group belongs to
that variety.

34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph