Reduced fusion systems over 2-groups of sectional rank at most four
Bob Oliver

Abstract:
We classify all reduced, indecomposable fusion systems over finite 
2-groups of sectional rank at most four.  The resulting list is very 
similar to that by Gorenstein and Harada of all simple groups of sectional 
2-rank at most four.  But our method of proof is very different from 
theirs, and is based on an analysis of the essential subgroups which can 
occur in the fusion systems.