We use tools from combinatorial group theory in order to study actions of three types on groups acting on a curve, namely the automorphism group of a compact Riemann surface, the mapping class group acting on a surface (which now is allowed to have some points removed) and the absolute Galois group $$\mathrm {Gal}({\bar{{\mathbb {Q}}}}/{\mathbb {Q}})$$ Gal ( Q ¯ / Q ) in the case of cyclic covers of the projective line.

中文翻译：

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射影线循环覆盖上的组动作

我们使用组合群论的工具来研究作用在曲线上的三类群的作用，即紧黎曼曲面的自同构群，作用在曲面上的映射类群（现在允许去除一些点） ) 和绝对伽罗瓦群 $$\mathrm {Gal}({\bar{{\mathbb {Q}}}}/{\mathbb {Q}})$$ Gal ( Q¯ / Q ) 在循环的情况下投影线的封面。