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The theory of fusion systems : an algebraic approach / David A. Craven.

By: Material type: TextTextSeries: Cambridge studies in advanced mathematics ; 131.Publisher: Cambridge : Cambridge University Press, 2011Description: 1 online resource (xii, 371 pages) : digital, PDF file(s)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780511794506 (ebook)
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 512/.23 22
LOC classification:
  • QA177 .C73 2011
Online resources:
Contents:
Machine generated contents note: 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.
Summary: 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.
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Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Machine generated contents note: 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.

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.

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