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Softcover ISBN:  9781470456658 
Product Code:  CONM/765 
List Price:  $122.00 
MAA Member Price:  $109.80 
AMS Member Price:  $97.60 
eBook ISBN:  9781470464219 
Product Code:  CONM/765.E 
List Price:  $122.00 
MAA Member Price:  $109.80 
AMS Member Price:  $97.60 
Softcover ISBN:  9781470456658 
eBook ISBN:  9781470464219 
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 DetailsContemporary MathematicsVolume: 765; 2021; 444 ppMSC: 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 2fusion 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 twopart program. The first part of the program aims to determine a large subclass of the class of simple 2fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
ReadershipGraduate 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 28 in Chapters 615, 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


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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 2fusion 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 twopart program. The first part of the program aims to determine a large subclass of the class of simple 2fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
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 28 in Chapters 615, 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