Reduced fusion systems over <i>p</i>-groups with abelian subgroup of index <i>p</i>: II

Abstract

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