Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Hom-Groups and Hom-Group actions   A Hom-group is the non-associative generalization of a group, whose
associativity and unitality are twisted by a compatible bijective map. In this
paper, we give some new examples of Hom-groups, and show the first and the
second isomorphism fundamental theorems of homomorphisms on Hom-groups. We also
introduce the notion of Hom-group action, and as an application, we show the
first Sylow theorem for Hom-groups along the line of group actions.

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The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex