The Classification of the Finite Simple Groups

9401852 里昂 该项目支持有限简单群分类证明的修订工作。 主要研究者建议：（1）开始出版，从介绍部分开始，给出系列的大纲，并为后面的部分奠定一般的群论和K-群论基础;同时（2）继续写后面的部分，其中大部分章节的草稿已经存在。 一个群是一个具有单一运算的代数结构。 它出现在数学、物理和化学的许多领域。 有限群的基本构造块是有限单群。 在过去的十年中，数学的主要成果之一是有限单群的分类，证明它需要10，000到15，000页的期刊。 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明。

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.