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Quaternion Fusion Packets
 
Michael Aschbacher California Institute of Technology, Pasadena, CA
Quaternion Fusion Packets
Softcover ISBN:  978-1-4704-5665-8
Product Code:  CONM/765
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
eBook ISBN:  978-1-4704-6421-9
Product Code:  CONM/765.E
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
Softcover ISBN:  978-1-4704-5665-8
eBook: ISBN:  978-1-4704-6421-9
Product Code:  CONM/765.B
List Price: $244.00 $183.00
MAA Member Price: $219.60 $164.70
AMS Member Price: $195.20 $146.40
Quaternion Fusion Packets
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Quaternion Fusion Packets
Michael Aschbacher California Institute of Technology, Pasadena, CA
Softcover ISBN:  978-1-4704-5665-8
Product Code:  CONM/765
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
eBook ISBN:  978-1-4704-6421-9
Product Code:  CONM/765.E
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
Softcover ISBN:  978-1-4704-5665-8
eBook ISBN:  978-1-4704-6421-9
Product Code:  CONM/765.B
List Price: $244.00 $183.00
MAA Member Price: $219.60 $164.70
AMS Member Price: $195.20 $146.40
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 7652021; 444 pp
    MSC: Primary 20

    Let \(p\) be a prime and \(S\) a finite \(p\)-group. A \(p\)-fusion system on \(S\) is a category whose objects are the subgroups of \(S\) and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory.

    The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.

    Readership

    Graduate students and research mathematicians interested in the theory of finite groups.

  • Table of Contents
     
     
    • Chapters
    • Michael Aschbacher — Quanternion Fusion Packets
  • Additional Material
     
     
  • Reviews
     
     
    • Aschbacher has done a fine job of providing a careful overview and development of background results with supporting examples in Chapters 1 through 5 of this volume, before plunging into the proofs of the main supporting Theorems 2-8 in Chapters 6-15, and concluding with the proofs of Theorem 1 and the Main Theorem in Chapter 16. The pace and intensity of work on the classification of the finite simple groups during the 1970s were extraordinary. In consequence, exposition often suffered. Aschbacher has ably remedied this in the current volume, for which he deserves much thanks.

      Ronald Solomon, Ohio State University
  • 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: 7652021; 444 pp
MSC: Primary 20

Let \(p\) be a prime and \(S\) a finite \(p\)-group. A \(p\)-fusion system on \(S\) is a category whose objects are the subgroups of \(S\) and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory.

The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.

Readership

Graduate students and research mathematicians interested in the theory of finite groups.

  • Chapters
  • Michael Aschbacher — Quanternion Fusion Packets
  • Aschbacher has done a fine job of providing a careful overview and development of background results with supporting examples in Chapters 1 through 5 of this volume, before plunging into the proofs of the main supporting Theorems 2-8 in Chapters 6-15, and concluding with the proofs of Theorem 1 and the Main Theorem in Chapter 16. The pace and intensity of work on the classification of the finite simple groups during the 1970s were extraordinary. In consequence, exposition often suffered. Aschbacher has ably remedied this in the current volume, for which he deserves much thanks.

    Ronald Solomon, Ohio State University
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.