Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Schur p-groups of odd order   A finite group $G$ is called a Schur group if any $S$-ring over $G$ is
associated in a natural way with a subgroup of $Sym(G)$ that contains all right
translations. We prove that the groups $\mathbb{Z}_3\times \mathbb{Z}_{3^n}$,
where $n\geq 1$, are Schur. Modulo previously obtained results, it follows that
every noncyclic Schur $p$-group, where $p$ is an odd prime, is isomorphic to
$\mathbb{Z}_3\times \mathbb{Z}_3 \times \mathbb{Z}_3$ or $\mathbb{Z}_3\times
\mathbb{Z}_{3^n}$, $n\geq 1$ .

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg