Moufang Sets - Split BN-pairs of Rank one

本项目的目的是研究牟方集。它们可以被看作是一级的Moufang建筑。在群论中，Moufang集是双传递置换群，使得点稳定子包含正则正规子群。我们计划研究三种类型的问题/问题：通过研究Moufang集上的有限双传递置换群，研究具有秩为1的分裂BN对的双传递置换群的分类。给一个Moufang集。集合上是否有条件暗示它有特殊的元素，甚至有特殊的子Moufang集合？给出了交换Moufang集的一个性质。我们能把它推广到2类、3类或任意类的幂零Moufang集吗？问题（c）的目的是证明类2或类3的幂零Moufang集。特别是，我们计划进一步探讨的结构，例外的代数群的相对秩为1。

The aim of the project is to study Moufang sets. They can be seen as rank one Moufang buildings. In the language of group theory Moufang sets are doubly transitive permutation groups such that the point stabilizer contains a regular normal subgroup. We plan to investigate three types of questions/issues: Simplify the classification of finite doubly transitive groups with a split BN-pair of rank one by studying these doubly transitive permutation groups in the setting of Moufang sets. Given a Moufang set. Are there conditions on the set implying that it has special elements or even a special sub-Moufang set? Given a property of an abelian Moufang set. Can we generalise it to nilpotent Moufang sets of class 2 or 3 or arbitrary class? Question (c) aims to characterise the nilpotent Moufang sets of class 2 or 3. In particular, we plan to further explore the structure of the exceptional algebraic groups of relative rank one.