Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type

Description

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 $\mathrm{Out}(G)$. Contents Abstract Automorphisms of Fusion Systemsof Finite Simple Groups of Lie Type Introduction Chapter 1. Tame and reduced fusion systems Chapter 2. Background on finite groups of Lie type Chapter 3. Automorphisms of groups of Lie type Chapter 4. The equicharacteristic case Chapter 5. The cross characteristic case: I Chapter 6. The cross characteristic case: II Appendix A. Injectivity of μG Bibliography for Automorphisms of Fusion Systems of Finite Simple Groups of Lie Type Automorphisms of Fusion Systems of Sporadic Simple Groups Introduction Chapter 1. Automorphism groups of fusion systems: Generalities Chapter 2. Automorphisms of 2-fusion systems of sporadic groups Chapter 3. Tameness at odd primes Chapter 4. Tools for comparing automorphisms of fusion and linking systems Chapter 5. Injectivity of μG Bibliography for Automorphisms of Fusion Systems of Sporadic Simple Groups Página em branco