Automorphisms of fusion systems of finite simple groups of lie type Automorphisms of fusion systems of sporadic simple groups

Author(s)

Bibliographic Information

Automorphisms of fusion systems of finite simple groups of lie type . Automorphisms of fusion systems of sporadic simple groups

Carles Broto, Jesper M. Moller, Bob Oliver . Bob Oliver

(Memoirs of the American Mathematical Society, no. 1267)

American Mathematical Society, c2019

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Note

"November 2019, volume 262, number 1267 (fourth of 7 numbers)"

Includes bibliographical reference (p. 115-117, 161-163)

Description and Table of Contents

Description

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

Introduction Tame and reduced fusion systems Background on finite groups of Lie type Automorphisms of groups of Lie type The equicharacteristic case The cross characteristic case: I The cross characteristic case: II Appendix A. Injectivity of $\mu _G$ by Bob Oliver Bibliography.

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Details

  • NCID
    BB29726031
  • ISBN
    • 9781470437725
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Providence, R.I.
  • Pages/Volumes
    vi, 163 p.
  • Size
    26 cm
  • Parent Bibliography ID
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