This research is concerned with the correction, clarification and simplification of the classification of finite simple groups. 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 finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. The research supported is a joint effort with Gorenstein and Lyons of Rutgers University to produce a self-contained, simplified and coherent treatment of the classification proof in a space of approximately 3000 pages.
