Authors: Bob Oliver and Albert Ruiz

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

Abstract: 
We finish the classification, begun in two earlier papers, of all simple 
fusion systems over finite nonabelian $p$-groups with an abelian subgroup 
of index $p$. In particular, this gives many new examples illustrating the 
enormous variety of exotic examples that can arise. In addition, we 
classify all simple fusion systems over infinite nonabelian discrete 
$p$-toral groups with an abelian subgroup of index $p$. In all of these 
cases (finite or infinite), we reduce the problem to one of listing all 
$\mathbb{F}_pG$-modules (for $G$ finite) satisfying certain conditions: a 
problem which was solved in an earlier paper by Craven, Oliver, and 
Semeraro using the classification of finite simple groups.

Status: Not yet submitted.