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Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

Carles Broto, Jesper M. Moller, Bob Oliver (Autoren)

Buch | Softcover

115 Seiten

2020
American Mathematical Society (Verlag)
978-1-4704-3772-5 (ISBN)

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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 $/mathrm{Out}(G)$.

Carles Broto, Universitat Autonoma de Barcelona, Bellaterra, Spain. Jesper M. Moller, Matematisk Institut, Kobenhavn, Denmark. Bob Oliver, Universite Paris 13, Villetaneuse, France.

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.

Erscheinungsdatum	31.12.2019
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	325 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-3772-4 / 1470437724
ISBN-13	978-1-4704-3772-5 / 9781470437725
Zustand	Neuware