The Classification of Finite Simple Groups

里昂/所罗门97-01253这个项目是一个延续的修订项目开始与丹尼Gorenstein的证明分类的有限简单的群体。提议者打算在赠款期内出版三卷（其中两卷已经出版）。第一个三是致力于奠定基础，建立许多性质的已知简单的群体所需的证明。第二章和第三章致力于各种唯一性定理，证明的关键基础定理。在第二个将是本德的强嵌入子群定理和变化;新定理的p-分量唯一性子群;和一个版本的全球C（G，T）定理，部分合作理查德富特。在第三将是准备定理的唯一性情况下，组的甚至类型，连接p-唯一性和2-唯一性的情况下，从合并理论的角度来看，写的Gernot斯特罗特。 有限单群在一个不断加速的过程中被分类，这个过程在1980年左右达到高潮，证明依赖于数百篇文章，总计数万页。由于这一结果在群论及其许多应用中的中心地位，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明，尽可能直接和清晰，并使用目前最好的想法。证明现在被认为是一个系列的大约10卷，其中前两个已经出现。

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.