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arXiv · 1604.04415

The Grothendieck-Teichmüller group of $PSL(2, q)$

Pierre Guillot
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Abstract

We show that the Grothendieck-Teichmüller group of $PSL(2, q)$, or more precisely the group $GT_1(PSL(2, q))$ as previously defined by the author, is the product of an elementary abelian 2-group and several copies of the dihedral group of order 8. Moreover, when $q$ is even, we show that it is trivial. We explain how it follows that the moduli field of any "dessin d'enfant" whose monodromy group is $PSL(2, q)$ has derived length less than 4. This paper can serve as an introduction to the general results on the Grothendieck-Teichmüller group of finite groups obtained by the author.

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Pierre Guillot. 2016-04-15. The Grothendieck-Teichmüller group of $PSL(2, q)$. https://arxiv.org/abs/1604.04415

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