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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 Synopsis

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 $\mathrm{Out}(G)$.

About This Edition

ISBN: 9781470437725
Publication date:
Author: Carles Broto, Jesper Møller, Robert Oliver
Publisher: American Mathematical Society
Format: Paperback
Pagination: 115 pages
Series: Memoirs of the American Mathematical Society
Genres: Algebraic geometry
Algebra