Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite groups with coprime fixed-point-free automorphisms and
  applications   We study a class of finite groups $G$ which behave similarly to elementary
abelian $p$-groups with $p$ prime, that is, there exists a subgroup $N$ such
that all elements of $G\setminus N$ are conjugate or inverse-conjugate under
$\Aut(G)$. In this paper, we show that such groups are solvable. As an
application, we characterise a class of normal edge-transitive Cayley graphs of
$G$, which are complete multipartite graphs.

1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th