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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society SeriesPublisher: Providence : American Mathematical Society, 2019Copyright date: ©2019Edition: 1st edDescription: 1 online resource (176 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470455071
Subject(s): Genre/Form: Additional physical formats: Print version:: Automorphisms of Fusion Systems of Finite Simple Groups of Lie TypeDDC classification:
  • 512.20000000000005
LOC classification:
  • QA177 .B768 2019
Online resources:
Contents:
Cover -- Title page -- Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver -- Introduction -- Tables of substitutions for Theorem B -- Chapter 1. Tame and reduced fusion systems -- Chapter 2. Background on finite groups of Lie type -- Chapter 3. Automorphisms of groups of Lie type -- Chapter 4. The equicharacteristic case -- Chapter 5. The cross characteristic case: I -- Chapter 6. The cross characteristic case: II -- Appendix A. Injectivity of _{ } by Bob Oliver -- A.1. Classical groups of Lie type in odd characteristic -- A.2. Exceptional groups of Lie type in odd characteristic -- Bibliography for Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type -- Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver -- Introduction -- Chapter 1. Automorphism groups of fusion systems: Generalities -- Chapter 2. Automorphisms of 2-fusion systems of sporadic groups -- Chapter 3. Tameness at odd primes -- Chapter 4. Tools for comparing automorphisms of fusion and linking systems -- Chapter 5. Injectivity of _{ } -- Bibliography for Automorphisms of Fusion Systems of Sporadic Simple Groups -- Back Cover.
Summary: 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).
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Cover -- Title page -- Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type by Carles Broto, Jesper M. Møller, and Bob Oliver -- Introduction -- Tables of substitutions for Theorem B -- Chapter 1. Tame and reduced fusion systems -- Chapter 2. Background on finite groups of Lie type -- Chapter 3. Automorphisms of groups of Lie type -- Chapter 4. The equicharacteristic case -- Chapter 5. The cross characteristic case: I -- Chapter 6. The cross characteristic case: II -- Appendix A. Injectivity of _{ } by Bob Oliver -- A.1. Classical groups of Lie type in odd characteristic -- A.2. Exceptional groups of Lie type in odd characteristic -- Bibliography for Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type -- Automorphisms of Fusion Systems of Sporadic Simple Groups by Bob Oliver -- Introduction -- Chapter 1. Automorphism groups of fusion systems: Generalities -- Chapter 2. Automorphisms of 2-fusion systems of sporadic groups -- Chapter 3. Tameness at odd primes -- Chapter 4. Tools for comparing automorphisms of fusion and linking systems -- Chapter 5. Injectivity of _{ } -- Bibliography for Automorphisms of Fusion Systems of Sporadic Simple Groups -- Back Cover.

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).

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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