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The Generalized Fitting Subsystem of a Fusion System
 
Michael Aschbacher California Institute of Technology, Pasadena, CA
The Generalized Fitting Subsystem of a Fusion System
eBook ISBN:  978-1-4704-0600-4
Product Code:  MEMO/209/986.E
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $44.40
The Generalized Fitting Subsystem of a Fusion System
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The Generalized Fitting Subsystem of a Fusion System
Michael Aschbacher California Institute of Technology, Pasadena, CA
eBook ISBN:  978-1-4704-0600-4
Product Code:  MEMO/209/986.E
List Price: $74.00
MAA Member Price: $66.60
AMS Member Price: $44.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2092011; 110 pp
    MSC: 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 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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2092011; 110 pp
MSC: 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 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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