The Theory of Fusion Systems : an Algebraic Approach.
The first book to deal comprehensively with the theory of fusion systems.
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| Online Access: | Electronic book from EBSCO |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: | Cambridge : Cambridge University Press, 2011. |
| Series: | Cambridge Studies in Advanced Mathematics, 131.
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| Subjects: |
Table of Contents:
- 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.
- 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.
- 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.
- 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.