The Theory of Fusion Systems: An Algebraic Approach [Hardcover]

The first book to deal comprehensively with the theory of fusion systems.This is the first book to deal with the new and expanding field of fusion systems, of increasing importance both to algebraists and topologists. Designed for use as a text and reference work, it is suitable for graduate students and experts alike.This is the first book to deal with the new and expanding field of fusion systems, of increasing importance both to algebraists and topologists. Designed for use as a text and reference work, it is suitable for graduate students and experts alike.Fusion systems are a recent development in finite group theory and sit at the intersection of algebra and topology. This book is the first to deal comprehensively with this new and expanding field, taking the reader from the basics of the theory right to the state of the art. Three motivational chapters, indicating the interaction of fusion and fusion systems in group theory, representation theory and topology are followed by six chapters that explore the theory of fusion systems themselves. Starting with the basic definitions, the topics covered include: weakly normal and normal subsystems; morphisms and quotients; saturation theorems; results about control of fusion; and the local theory of fusion systems. At the end there is also a discussion of exotic fusion systems. Designed for use as a text and reference work, this book is suitable for graduate students and experts alike.Preface; Part I. Motivation: 1. Fusion in finite groups; 2. Fusion in representation theory; 3. Fusion in topology; Part II. The Theory: 4. Fusion systems; 5. Weakly normal subsystems, quotients, and morphisms; 6. Proving saturation; 7. Control in fusion systems; 8. Local theory of fusion systems; 9. Exotic fusion systems; References; Index of notation; Index. Craven's efforts to collect together in one work all of the main achievements stem from an excellent intention, and the book establishes a unified terminology for fusion systems, l#²