Classification of Finite Simple Groups (eBook)

The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the "e;even case"e;, where the main groups arising are Lie-type (matrix) groups over a field of characteristic 2. The book thus completes a project begun by Daniel Gorenstein's 1983 book, which outlined the classification of groups of "e;noncharacteristic 2 type"e;. However, this book provides much more. Chapter 0 is a modern overview of the logical structure of the entire classification. Chapter 1 is a concise but complete outline of the "e;odd case"e; with updated references, while Chapter 2 sets the stage for the remainder of the book with a similar outline of the "e;even case"e;. The remaining six chapters describe in detail the fundamental results whose union completes the proof of the classification theorem. Several important subsidiary results are also discussed. In addition, there is a comprehensive listing of the large number of papers referenced from the literature. Appendices provide a brief but valuable modern introduction to many key ideas and techniques of the proof. Some improved arguments are developed, along with indications of new approaches to the entire classification-such as the second and third generation projects-although there is no attempt to cover them comprehensively. The work should appeal to a broad range of mathematicians-from those who just want an overview of the main ideas of the classification, to those who want a reader's guide to help navigate some of the major papers, and to those who may wish to improve the existing proofs.