eBook ISBN:  9781470406004 
Product Code:  MEMO/209/986.E 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $44.40 
eBook ISBN:  9781470406004 
Product Code:  MEMO/209/986.E 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $44.40 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 209; 2011; 110 ppMSC: Primary 20; 55
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 Lbalance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a JordonHölder theorem for fusion systems.

Table of Contents

Chapters

Introduction

1. Background

2. Direct products

3. $\mathcal {E}_{1}\wedge \mathcal {E}_{2}$

4. The product of strongly closed subgroups

5. Pairs of commuting strongly closed subgroups

6. Centralizers

7. Characteristic and subnormal subsystems

8. $T\mathcal {F}_{0}$

9. Components

10. Balance

11. The fundamental group of $\mathcal {F}^{c}$

12. Factorizing morphisms

13. Composition series

14. Constrained systems

15. Solvable fusion systems

16. Fusion systems in simple groups

17. An example


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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 Lbalance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a JordonHölder theorem for fusion systems.

Chapters

Introduction

1. Background

2. Direct products

3. $\mathcal {E}_{1}\wedge \mathcal {E}_{2}$

4. The product of strongly closed subgroups

5. Pairs of commuting strongly closed subgroups

6. Centralizers

7. Characteristic and subnormal subsystems

8. $T\mathcal {F}_{0}$

9. Components

10. Balance

11. The fundamental group of $\mathcal {F}^{c}$

12. Factorizing morphisms

13. Composition series

14. Constrained systems

15. Solvable fusion systems

16. Fusion systems in simple groups

17. An example