Automorphisms of fusion systems of sporadic simple groups



Bob Oliver



Abstract: We prove here that with a very small number of exceptions, when 

$G$ is a sporadic simple group and $p$ is a prime such that the $p$-fusion 

system of $G$ is simple, then $Out(G)$ is isomorphic to the outer 

automorphism groups of the fusion and linking systems of $G$. In 

particular, the $p$-fusion system of $G$ is tame in the sense of [AOV1], 

and is tamely realized by $G$ itself except when $G\cong M_{11}$ and $p=2$. 

From the point of view of homotopy theory, these results also imply that 

$Out(G)\cong Out(BG^\wedge_p)$ in many (but not all) cases.



Status: submitted