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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type
 
Carles Broto :  Universitat Autónoma de Barcelona, Bellaterra, Spain
Jesper M. Møller :  Matematisk Institut, København, Denmark
Bob Oliver :  Université Paris 13, Villetaneuse, France
Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type
Softcover ISBN:  978-1-4704-3772-5
Product Code:  MEMO/262/1267
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5507-1
Product Code:  MEMO/262/1267.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3772-5
eBook: ISBN:  978-1-4704-5507-1
Product Code:  MEMO/262/1267.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
Add to cart
Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type
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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type
Carles Broto :  Universitat Autónoma de Barcelona, Bellaterra, Spain
Jesper M. Møller :  Matematisk Institut, København, Denmark
Bob Oliver :  Université Paris 13, Villetaneuse, France
Softcover ISBN:  978-1-4704-3772-5
Product Code:  MEMO/262/1267
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
eBook ISBN:  978-1-4704-5507-1
Product Code:  MEMO/262/1267.E
List Price: $81.00
MAA Member Price: $72.90
AMS Member Price: $48.60
Softcover ISBN:  978-1-4704-3772-5
eBook ISBN:  978-1-4704-5507-1
Product Code:  MEMO/262/1267.B
List Price: $162.00 $121.50
MAA Member Price: $145.80 $109.35
AMS Member Price: $97.20 $72.90
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 262; 2019; 115 pp
    MSC: Primary 20; Secondary 55

    For a finite group \(G\) of Lie type and a prime \(p\), the authors compare the automorphism groups of the fusion and linking systems of \(G\) at \(p\) with the automorphism group of \(G\) itself. When \(p\) is the defining characteristic of \(G\), they are all isomorphic, with a very short list of exceptions. When \(p\) is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from \(\mathrm{Out}(G)\) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of \(BG^\wedge _p\) in terms of \(\mathrm{Out}(G)\).
  • Table of Contents
     
     
    • Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver
    • Introduction
    • 1. Tame and reduced fusion systems
    • 2. Background on finite groups of Lie type
    • 3. Automorphisms of groups of Lie type
    • 4. The equicharacteristic case
    • 5. The cross characteristic case: I
    • 6. The cross characteristic case: II
    • 7. Injectivity of $\mu _G$ by Bob Oliver
    • Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver
    • Introduction
    • 8. Automorphism groups of fusion systems: Generalities
    • 9. Automorphisms of $2$-fusion systems of sporadic groups
    • 10. Tameness at odd primes
    • 11. Tools for comparing automorphisms of fusion and linking systems
    • 12. Injectivity of $\mu _G$
  • 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
Memoirs of the American Mathematical Society
Volume: 262; 2019; 115 pp
MSC: Primary 20; Secondary 55

For a finite group \(G\) of Lie type and a prime \(p\), the authors compare the automorphism groups of the fusion and linking systems of \(G\) at \(p\) with the automorphism group of \(G\) itself. When \(p\) is the defining characteristic of \(G\), they are all isomorphic, with a very short list of exceptions. When \(p\) is different from the defining characteristic, the situation is much more complex but can always be reduced to a case where the natural map from \(\mathrm{Out}(G)\) to outer automorphisms of the fusion or linking system is split surjective. This work is motivated in part by questions involving extending the local structure of a group by a group of automorphisms, and in part by wanting to describe self homotopy equivalences of \(BG^\wedge _p\) in terms of \(\mathrm{Out}(G)\).
  • Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver
  • Introduction
  • 1. Tame and reduced fusion systems
  • 2. Background on finite groups of Lie type
  • 3. Automorphisms of groups of Lie type
  • 4. The equicharacteristic case
  • 5. The cross characteristic case: I
  • 6. The cross characteristic case: II
  • 7. Injectivity of $\mu _G$ by Bob Oliver
  • Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver
  • Introduction
  • 8. Automorphism groups of fusion systems: Generalities
  • 9. Automorphisms of $2$-fusion systems of sporadic groups
  • 10. Tameness at odd primes
  • 11. Tools for comparing automorphisms of fusion and linking systems
  • 12. Injectivity of $\mu _G$
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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