Moufang Sets - Split BN-pairs of Rank one

该项目的目的是研究牟方集。它们可以被视为牟坊一级建筑。在群论的语言中，Moufang集是双传递置换群，使得点稳定子包含正则正规子群。我们计划研究三类问题：通过研究Moufang集上的双传递置换群，简化具有秩1的分裂BN对的有限双传递群的分类。给出了一套Moufang。集合上有没有条件暗示它有特殊的元素，甚至有特殊的子牟房集？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)的目的是刻画类2或类3的幂零Moufang集。特别地，我们计划进一步研究相对秩为1的例外代数群的结构。

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.