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Softcover ISBN:  9781470437725 
Product Code:  MEMO/262/1267 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470455071 
Product Code:  MEMO/262/1267.E 
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MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470437725 
eBook ISBN:  9781470455071 
Product Code:  MEMO/262/1267.B 
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MAA Member Price:  $145.80 $109.35 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 262; 2019; 115 ppMSC: 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 $\mu _G$


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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 $\mu _G$