$PSL(2, q)$的Grothendieck-Teichmüller群
The Grothendieck-Teichmüller group of $PSL(2, q)$
摘要：
我们证明了$PSL(2, q)$的Grothendieck-Teichmüller群，或者更准确地说，作者以前定义的群$GT_1(PSL(2, q))$，是一个初等交换2-群和几个8阶二面体群的副本的乘积。此外，当$q$为偶数时，我们证明了它是平凡的.我们解释它如何遵循的模字段的任何“dessin d 'enfant”的monodromy组是$PSL(2, q)$已导出长度小于4。本文可作为作者对有限群的Grothendieck-Teichmüller群的一般结果的介绍。
英文摘要：
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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