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The Theory of Fusion Systems : an Algebraic Approach.
The first book to deal comprehensively with the theory of fusion systems.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2011.
|
| Colección: | Cambridge Studies in Advanced Mathematics, 131.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Craven, David A. | |
| 245 | 1 | 4 | |a The Theory of Fusion Systems : |b an Algebraic Approach. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2011. | ||
| 300 | |a 1 online resource (386 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Cambridge Studies in Advanced Mathematics, 131 | |
| 505 | 0 | |a Cover; THE THEORY OF FUSION SYSTEMS; CAMBRIDGE STUDIES IN ADVANCED MATHEMATICS; Title; Copyright; Contents; Preface; Part I: Motivation; 1 Fusion in finite groups; 1.1 Control of fusion; 1.2 Normal p-complements; 1.3 Alperin's fusion theorem; 1.4 The focal subgroup theorem; 1.5 Fusion systems; Exercises; 2 Fusion in representation theory; 2.1 Blocks of finite groups; 2.2 The Brauer morphism and relative traces; 2.3 Brauer pairs; 2.4 Defect groups and the?rst main theorem; 2.5 Fusion systems of blocks; Exercises; 3 Fusion in topology; 3.1 Simplicial sets; 3.2 Classifying spaces. | |
| 505 | 8 | |a 3.3 Simplicial and cosimplicial objects3.4 Bousfield-Kan completions; 3.5 The centric linking systems of groups; 3.6 Constrained fusion systems; Exercises; Part II: The theory; 4 Fusion systems; 4.1 Saturated fusion systems; 4.2 Normalizing and centralizing; 4.3 The equivalent definitions; 4.4 Local subsystems; 4.5 Centric and radical subgroups; 4.6 Alperin's fusion theorem; 4.7 Weak and strong closure; Exercises; 5 Weakly normal subsystems, quotients, and morphisms; 5.1 Morphisms of fusion systems; 5.3 Normal subgroups; 5.4 Weakly normal subsystems; 5.2 The isomorphism theorems. | |
| 505 | 8 | |a 5.5 Correspondences for quotients5.6 Simple fusion systems; 5.7 Soluble fusion systems; Exercises; 6 Proving saturation; 6.1 The surjectivity property; 6.2 Reduction to centric subgroups; 6.3 Invariant maps; 6.4 Weakly normal maps; Exercises; 7 Control in fusion systems; 7.1 Resistance; 7.2 Glauberman functors; 7.3 The ZJ-theorems; 7.4 Normal p-complement theorems; 7.5 The hyperfocal and residual subsystems; 7.6 Bisets; 7.7 The transfer; Exercises; 8 Local theory of fusion systems; 8.1 Normal subsystems; 8.2 Weakly normal and normal subsystems; 8.3 Intersections of subsystems. | |
| 505 | 8 | |a 8.4 Constraint and normal subsystems8.5 Central products; 8.6 The generalized Fitting subsystem; 8.7 L-balance; Exercises; 9 Exotic fusion systems; 9.1 Extraspecial p-groups; 9.2 The Solomon fusion system; 9.3 Blocks of finite groups; 9.4 Block exotic fusion systems; 9.5 Abstract centric linking systems; 9.6 Higher limits and centric linking systems; Exercises; References; Index of notation; Index. | |
| 520 | |a The first book to deal comprehensively with the theory of fusion systems. | ||
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references (pages 358-363) and indexes. | ||
| 546 | |a English. | ||
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Finite groups. | |
| 650 | 0 | |a Representations of algebras. | |
| 650 | 0 | |a Algebraic topology. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 6 | |a Représentations des algèbres. | |
| 650 | 6 | |a Topologie algébrique. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x General. |2 bisacsh | |
| 650 | 7 | |a Topología algebraica |2 embne | |
| 650 | 7 | |a Grupos finitos |2 embne | |
| 650 | 7 | |a Algebraic topology |2 fast | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Representations of algebras |2 fast | |
| 650 | 7 | |a Endliche Gruppe |2 gnd | |
| 650 | 7 | |a Algebraische Topologie |2 gnd | |
| 776 | 0 | 8 | |i Print version: |a Craven, David A. |t Theory of Fusion Systems : An Algebraic Approach. |d Cambridge : Cambridge University Press, ©2011 |z 9781107005969 |
| 830 | 0 | |a Cambridge Studies in Advanced Mathematics, 131. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=369453 |z Texto completo |
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