**Memoirs of the American Mathematical Society**

2011;
110 pp;
Softcover

MSC: Primary 20; 55;

Print ISBN: 978-0-8218-5303-0

Product Code: MEMO/209/986

List Price: $74.00

Individual Member Price: $44.40

**Electronic ISBN: 978-1-4704-0600-4
Product Code: MEMO/209/986.E**

List Price: $74.00

Individual Member Price: $44.40

# The Generalized Fitting Subsystem of a Fusion System

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*Michael Aschbacher*

The notion of a fusion system was first defined and explored by Puig, in the context of modular representation theory. Later, Broto, Levi, and Oliver extended the theory and used it as a tool in homotopy theory. The author seeks to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems. Among other results, he defines the notion of a simple system, the generalized Fitting subsystem of a fusion system, and prove the L-balance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a Jordon-Hölder theorem for fusion systems.

#### Table of Contents

# Table of Contents

## The Generalized Fitting Subsystem of a Fusion System

- Introduction 18 free
- Chapter 1. Background 714 free
- Chapter 2. Direct products 1118
- Chapter 3. E1E2 1724
- Chapter 4. The product of strongly closed subgroups 2330
- Chapter 5. Pairs of commuting strongly closed subgroups 2532
- Chapter 6. Centralizers 3340
- Chapter 7. Characteristic and subnormal subsystems 3946
- Chapter 8. TF0 4956
- Chapter 9. Components 6168
- Chapter 10. Balance 6774
- Chapter 11. The fundamental group of Fc 7178
- Chapter 12. Factorizing morphisms 7784
- Chapter 13. Composition series 8390
- Chapter 14. Constrained systems 8794
- Chapter 15. Solvable fusion systems 9198
- Chapter 16. Fusion systems in simple groups 95102
- Chapter 17. An example 105112
- Bibliography 109116