The Classification of Finite Simple Groups

Lyons/所罗门97-01253这个项目是丹尼·戈伦斯坦为证明有限单群的分类而开始的修正项目的继续。提出者考虑在赠款期间出版三卷(已经出版了两卷)。第一部分致力于为建立证明所需的已知单群的许多性质奠定基础。第二章和第三章致力于各种唯一性定理，它们是证明的关键基础定理。第二部分是Bender的强嵌入子群定理和变分；关于p-分支唯一性子群的新定理；以及部分与Richard Foote合作的整体C(G，T)-定理的一个版本。第三部分是Gernot Stroth所著的关于偶数型群的唯一性情形的准备定理，这些情形是由Gernot Stroth从合并理论的观点出发的连接p-唯一性和2-唯一性情形。有限单群在一个不断加速的过程中被分类，这个过程在1980年左右达到顶峰，这一证明依赖于数百篇文章，总计数万页。由于这一结果在群论中的中心地位和它的许多应用，以及证明的长度和复杂性，目前的努力开始了。目标是一个连贯的证据，尽可能直接和明确，并使用目前最好的想法。《证据》现在被构思为大约十卷的系列，其中前两卷已经出现。

LYONS/SOLOMON 97-01253 This project is a continuation of the revision project begun with Danny Gorenstein for the proof of the classification of the finite simple groups. The proposers contemplate publishing three volumes during the period of the grant(two already having been published). The first of the three is devoted to laying the groundwork for establishing the many properties of the known simple groups necessary for the proof. The second and third are devoted to various uniqueness theorems, the key underlying theorems for the proof. In the second will be Bender's strongly embedded subgroup theorem and variations; new theorems on p-component uniqueness subgroups; and a version of the global C(G,T)-theorem, partly in collaboration with Richard Foote. In the third will be preparation theorems for the uniqueness case for groups of even type, connecting p-uniqueness and 2- uniqueness case from an amalgam-theoretic point of view, written by Gernot Stroth. The finite simple groups were classified in an ever-accelerating process which culminated around 1980, in a proof depending on hundreds of articles totaling tens of thousands of pages. Because of the central position of this result in group theory and its many applications, as well as the length and complexity of the proof, the current effort was begun. The goal is a coherent proof, as direct and clear as possible and using the best ideas at present. The proof is now conceived as a series of roughly ten volumes, of which the first two have already appeared.