Authors: C. Broto, J. Møller, B. Oliver

Title: Automorphisms of fusion systems of finite simple groups of Lie type

Abstract: For a finite group $G$ of Lie type and a prime $p$, we 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 $\Out(G)$ 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 $BG\pcom$ in terms of $\Out(G)$.

Status: (just) submitted