Reduced Fusion Systems Over 2-Groups of Sectional Rank at Most 4

The author classifies all reduced, indecomposable fusion systems over finite $2$-groups of sectional rank at most $4$. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional $2$-rank at most $4$. But this 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.