Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A group sum inequality and its application to power graphs   Let $G$ be a finite group of order $n$, and let $C_n$ be the cyclic group of
order $n$. We show that $\sum_{g \in C_n} \phi(\mathrm{o}(g))\geq \sum_{g \in
G} \phi(\mathrm{o}(g))$, with equality if and only if $G$ is isomorphic to
$C_n$. As an application, we show that among all finite groups of a given
order, the cyclic group of that order has the maximum number of undirected
edges in its directed power graph.

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The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
14
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: gr-qc
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs