The Classification of the Finite Simple Groups

9401852莱昂斯这个项目支持继续修订有限单群分类的证明。主要调查人员建议(1)开始出版，首先从介绍该系列的概述开始，并为后面的部分奠定一般的群论和K-群论基础；同时(2)继续编写后面的部分，其中大多数章节的草稿已经存在。群是具有单一运算的代数结构。它出现在许多数学领域，也出现在物理和化学领域。有限群的基本构件是有限单群。过去十年数学中的主要结果之一是有限单群的分类，要证明这一点需要10,000到15,000页的期刊页。所支持的研究是一项共同努力，以产生一个独立的，简化的和连贯的处理这一证据。

9401852 Lyons This project supports continued work on the revision of the proof of the classification of finite simple groups. The principal investigators propose (1) to begin its publication, starting with the introductory sections giving an outline of the series and laying the general group-theoretic and K-group-theoretic foundations for the later parts; and at the same time (2) to continue the writing of the later parts, for which drafts of most chapters already exist. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. The research supported is a joint effort to produce a self-contained, simplified and coherent treatment of this proof.