The goal is to outline the original proof of the classification of the finite simple groups for non-specialist readers. The project began with Daniel Gorenstein's 1983 book with the same title, but designated volume one. It addressed groups of non-characteristic 2 type. This is the second volume, and discusses the treatment of groups of characteristic 2 type. Among the topics are the classification of groups of Gorenstein-Walter type, the classification of quasi-thin groups, the pre-trichotomy and trichotomy theorems, and eliminating the uniqueness case. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
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Michael Aschbacher, California Institute of Technology, Pasadena, CA||Richard Lyons, Rutgers University, Piscataway, NJ|Stephen D. Smith, University of Illinois at Chicago, IL|Ronald Solomon, The Ohio State University, Columbus, O
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Hardback. Zustand: New. The book provides an outline and modern overview of the classification of the finite simple groups. It primarily covers the "even case", 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 "noncharacteristic 2 type". 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 "odd case" with updated references, while Chapter 2 sets the stage for the remainder of the book with a similar outline of the "even case". 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. Bestandsnummer des Verkäufers LU-9780821853368
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