Permutation groups where non-trivial elements have few fixed points

在我们合作的第一阶段，Kay Magaard和我取得了一些不错的成果，并提出了一些更精确的问题，我们计划在2014年回答这些问题。我们项目的基础是Schoeneberg的结果。它说在代数曲线的非平凡自同构中，固定至少五个点的所有不动点都是Weierstrass点。带着这个定理，Kay Magaard和我开始研究置换群，其中每个非平凡元素都有几个不动点，因此阻碍了用Schoeneberg的结果找到Weierstrass点。我们的目标是了解这类群的结构，并对具有这一性质的简单群进行完全的分类。

During the first phase of our cooperation Kay Magaard and I produced a few good results and some more precise questions emerged that we plan to answer in 2014.The basis of our project is a result of Schoeneberg's. It says that all fixed points of a non-trivial automorphism of an algebraic curve that fixes at least five points is a Weierstrass point.With this theorem in mind, Kay Magaard and I started to investigate permutation groups where every non-trivial element has few fixed points, hence being an obstruction to finding Weierstrass points with Schoeneberg's result. It is our aim to understand the structure of such groups and to classify the simple groups with this property completely.