Moufang Sets - Split BN-pairs of Rank one

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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.