Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphism groups of dessins d'enfants   Recently, Gareth Jones observed that every finite group $G$ can be realized
as the group of automorphisms of some dessin d'enfant ${\mathcal D}$. In this
paper, complementing Gareth's result, we prove that for every possible action
of $G$ as a group of orientation-preserving homeomorphisms on a closed
orientable surface of genus $g \geq 2$, there is a dessin d'enfant ${\mathcal
D}$ admitting $G$ as its group of automorphisms and realizing the given
topological action. In particular, this asserts that the strong symmetric genus
of $G$ is also the minimum genus action for it to acts as the group of
automorphisms of a dessin d'enfant of genus at least two.

34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs