All p-local finite groups of rank two for odd prime p

In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analisis of the possible saturated fusion systems in terms of the outer automorphism group ant the proper F-radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-local finite group, getting some new examples of these for p = 3.