Reduced fusion systems over $p$-groups with abelian subgroup of index $p$: II

David A. Craven, Bob Oliver, and Jason Semeraro

Let $p$ be an odd prime, and let $S$ be a $p$-group with a unique 
elementary abelian subgroup $A$ of index $p$. We classify the simple fusion 
systems over all such groups $S$ in which $A$ is essential. The resulting 
list, which depends on the classification of finite simple groups, includes 
a large variety of new, exotic simple fusion systems.

Status: [soon to be] submitted