Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian groups with a $p^2$-bounded subgroup, revisited   Let $R$ be a commutative local uniserial ring of length $n$, $p$ a generator
of the maximal ideal, and $k$ the radical factor field. The pairs $(B,A)$ where
$B$ is a finitely generated $R$-module and $A\subset B$ a submodule of $B$ such
that $p^mA=0$ form the objects in the category $S_m(R)$. We show that in case
$m=2$ the categories $S_m(R)$ are in fact quite similar to each other: If also
$R'$ is a commutative local uniserial ring of length $n$ and with radical
factor field $k$, then the categories $S_2(R)/\mathcal N_R$ and
$S_2(R')/\mathcal N_{R'}$ are equivalent for certain nilpotent categorical
ideals $N_R$ and $N_{R'}$. As an application, we recover the known
classification of all pairs $(B,A)$ where $B$ is a finitely generated abelian
group and $A\subset B$ a subgroup of $B$ which is $p^2$-bounded for a given
prime number $p$.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
19
The categories of this paper are: eess
9
The categories of this paper are: nlin