Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type (Memoirs of the American Mathematical Society) - Softcover

Carles Broto (author), Jesper M. Moller (author) & Bob Oliver (author)

Softcover

ISBN 10: 1470437724 ISBN 13: 9781470437725

Publisher: American Mathematical Society, 2019

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 title

About the Author

Carles Broto, Universitat Autonoma de Barcelona, Bellaterra, Spain.

Jesper M. Moller, Matematisk Institut, Kobenhavn, Denmark.

Bob Oliver, Universite Paris 13, Villetaneuse, France.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2019
• Language: English
• ISBN 10: 1470437724
• ISBN 13: 9781470437725
• Binding: Paperback
• Number of pages: 115