Saturated fusion systems over -groups

In this paper we study the saturated fusion systems over -groups S of order greater than . This study requires the analysis of the possible saturated fusion systems in terms of the -automorphisms of the possible -centric and -radical subgroups. Also, for each case in the classification, either S is resistant or is constrained. The classification identifies a large family of resistant groups complementing the results on resistant groups found by various authors such as Green-Minh, Stancu, and Diaz-Ruiz-Viruel. Moreover, the classification provides some interesting examples of saturated fusion systems which have an -essential abelian subgroup of index p.