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 $\mathrm{Out}(G)$.
- ISBN13 9781470437725
- Publish Date 30 June 2020
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 115
- Language English