The Classification of the Finite Simple Groups

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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.