The primary focus of this project is producing a unified, accessible treatment of the existence, uniqueness, and structure of the sporadic simple groups. In addition, the principal investigator will study the action of groups on finite simplicial complexes. 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 aimed at simplifying the treatment of the sporadic simple groups.
