Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Schur 2-groups   A finite group $G$ is called a Schur group, if any Schur ring over $G$ is the
transitivity module of a point stabilizer in a subgroup of $\sym(G)$ that
contains all right translations. We complete a classification of abelian
$2$-groups by proving that the group $\mZ_2\times\mZ_{2^n}$ is Schur. We also
prove that any non-abelian Schur $2$-group of order larger than $32$ is
dihedral (the Schur $2$-groups of smaller orders are known). Finally, in the
dihedral case, we study Schur rings of rank at most $5$, and show that the
unique obstacle here is a hypothetical S-ring of rank $5$ associated with a
divisible difference set.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: eess