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arXiv · 1811.07849

Automorphism groups of dessins d'enfants

Ruben A. Hidalgo
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Abstract

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.

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Ruben A. Hidalgo. 2018-11-19. Automorphism groups of dessins d'enfants. https://doi.org/10.1007/s00013-018-1222-9

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