Mathematical Sciences: Stable Groups

这个项目是关于Cherlin-Zil'ber猜想的， 指出有限莫利秩的单群是代数群 代数闭域上的群。 它有两个部分： （1）通过寻找潜在的反例来反驳猜想 （2）证明了关于好群的猜想 (i.e.,对于具有对合的简单群）。 这太雄心勃勃了， 并且主要重点将放在秩1和2的BN对上。 的 研究者期望能够扩展有限群方法 理论，并提出新的方法（如在联合工作， Borovik和DeBonis）。 群是代数的基本结构， 对称性的体现。 模型论是其中的一个主要分支 数学的基础。 调查员会把 方法从模型论承担一个突出的猜想， 群论 这个猜想本身很有趣，但也是因为 一个测试用例，看看这种类型的方法有多大用处。

This project is about the Cherlin-Zil'ber Conjecture, which states that a simple group of finite Morley rank is an algebraic group over an algebraically closed field. It has two parts: (1)Disprove the conjecture by finding a potential counter-example (a bad group) in SO3(R); (2)Prove the conjecture for good groups (i.e., for simple groups with involutions). This is too ambitious, and the main emphasis will be on BN-pairs of ranks 1 and 2. The investigator expects to be able to extend methods of finite group theory and come up with new methods (as was done in joint work with Borovik and DeBonis). Groups are basic structures of algebra, the mathematical embodiment of symmetry. Model theory is one of the main branches of the foundations of mathematics. The investigator will bring methods from model theory to bear upon an outstanding conjecture in group theory. The conjecture is interesting in itself but also as a test case to see how far methods of this type will avail.