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On Fusion Systems of Component Type
 
Michael Aschbacher California Institute of Technology, Pasadena, California
On Fusion Systems of Component Type
Softcover ISBN:  978-1-4704-3520-2
Product Code:  MEMO/257/1236
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-4955-1
Product Code:  MEMO/257/1236.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3520-2
eBook: ISBN:  978-1-4704-4955-1
Product Code:  MEMO/257/1236.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
On Fusion Systems of Component Type
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On Fusion Systems of Component Type
Michael Aschbacher California Institute of Technology, Pasadena, California
Softcover ISBN:  978-1-4704-3520-2
Product Code:  MEMO/257/1236
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-4955-1
Product Code:  MEMO/257/1236.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3520-2
eBook ISBN:  978-1-4704-4955-1
Product Code:  MEMO/257/1236.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2572019; 182 pp
    MSC: Primary 20; Secondary 55

    This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups.

    Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Preliminaries
    • 2. Some Lemmas on Fusion Systems
    • 3. Tight embedding
    • 4. More on tight embedding
    • 5. Split extensions
    • 6. Component combinatorics
    • 7. The proof of Theorem
    • 8. Terminal components
    • 9. Standard subsystems
  • Additional Material
     
     
  • 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: 2572019; 182 pp
MSC: Primary 20; Secondary 55

This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups.

Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.

  • Chapters
  • Introduction
  • 1. Preliminaries
  • 2. Some Lemmas on Fusion Systems
  • 3. Tight embedding
  • 4. More on tight embedding
  • 5. Split extensions
  • 6. Component combinatorics
  • 7. The proof of Theorem
  • 8. Terminal components
  • 9. Standard subsystems
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
Please select which format for which you are requesting permissions.