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

Abstract

In this paper we give a classification of the rank two p p -local finite groups for odd  p p . This study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group of the possible F \mathcal {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 p -local finite group, getting some new examples of these for  p = 3 p=3 .