The Theory of Fusion Systems: An Algebraic Approach

David A. Craven

doi:10.1017/CBO9780511794506

The Theory of Fusion Systems

An Algebraic Approach

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David A. Craven, University of Oxford

Publisher:: Cambridge University Press
Online publication date:: August 2012
Print publication year:: 2011
Online ISBN:: 9780511794506
DOI:: https://doi.org/10.1017/CBO9780511794506

Subjects:: Mathematics (general), Mathematics, Algebra
Series:: Cambridge Studies in Advanced Mathematics (131)

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The Theory of Fusion Systems
David A. Craven
Online ISBN: 9780511794506

Book DOI: https://doi.org/10.1017/CBO9780511794506
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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.

"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, limiting the spread of conflicting definitions."
Nadia P. Mazza, Mathematical Reviews

"This very welcome book originates from a workshop on fusion systems held at the University of Birmingham in 2007 and is one of the first two texts on the subject, appearing at approximately the same time... The book serves as an excellent introduction to the subject and a guide to up to the cutting edget of current research."
Charles W. Eaton, Mathematical Reviews

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The Theory of Fusion Systems

An Algebraic Approach

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xii

PART I - MOTIVATION
pp 1-2

1 - Fusion in finite groups
pp 3-25

2 - Fusion in representation theory
pp 26-54

3 - Fusion in topology
pp 55-90

PART II - THE THEORY
pp 91-92

4 - Fusion systems
pp 93-133

5 - Weakly normal subsystems, quotients, and morphisms
pp 134-187

6 - Proving saturation
pp 188-214

7 - Control in fusion systems
pp 215-269

8 - Local theory of fusion systems
pp 270-316

9 - Exotic fusion systems
pp 317-357

References
pp 358-363

Index of notation
pp 364-365

Index
pp 366-371

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The Theory of Fusion Systems

An Algebraic Approach

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Contents

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