Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Quantitative Characterizations of Certain Symplectic Groups   Given a finite group $G$, denote by ${\rm D}(G)$ the degree pattern of $G$
and by ${\rm OC}(G)$ the set of all order components of $G$. Denote by $h_{{\rm
OD}}(G)$ (resp. $h_{{\rm OC}}(G)$) the number of isomorphism classes of finite
groups $H$ satisfying conditions $|H|=|G|$ and ${\rm D}(H)={\rm D}(G)$ (resp.
${\rm OC}(H)={\rm OC}(G)$). A finite group $G$ is called OD-characterizable
(resp. OC-characterizable) if $h_{\rm OD}(G)=1$ (resp. $h_{\rm OC}(G)=1$). Let
$C=C_p(2)$ be a symplectic group over binary field, for which $2^p-1>7$ is a
Mersenne prime. The aim of this article is to prove that $h_{\rm
OD}(C)=1=h_{\rm OC}(C)$.

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The categories of this paper are: stat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph