Abstract Motivated by the theory of Riemann surfaces and specifically the significance of Weierstrass points, we study finite simple groups from a permutation action point of view. We classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most two fixed points on each non-regular orbit and at most four fixed points in total.

中文翻译：

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固定性2的有限简单置换群作为黎曼曲面的自同构群的出现

摘要 受黎曼曲面理论的启发，特别是魏尔斯特拉斯点的重要性，我们从置换作用的角度研究了有限单群。我们将有限单群忠实地作用于至少 2 的紧黎曼曲面上的所有可能性进行分类，使得所有非平凡元素在每个非规则轨道上最多有两个不动点，总共最多有四个不动点.