Author: Bob Oliver

Title: Reductions to simple fusion systems

Abstract: We prove that if $E$ is a centric, normal subsystem of a 
saturated fusion system $F$, and either $Aut_F(T)/Aut_E(T)$ or $Out(E)$ is 
$p$-solvable, then $F$ can be "reduced" to $E$ by alternately taking normal 
subsystems of $p$-power index or of index prime to $p$. In particular, this 
is the case whenever $E$ is simple and "tamely realized" by a known simple 
group. This answers a question posed by Michael Aschbacher, and is useful 
when analyzing involution centralizers in simple fusion systems, in 
connection with his program for reproving parts of the classification of 
finite simple groups by classifying certain 2-fusion systems. 

Status: submitted