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

Díaz, Antonio; Ruiz, Albert; Viruel, Antonio

doi:10.1090/S0002-9947-06-04367-4

All $p$-local finite groups of rank two for odd prime $p$
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by Antonio Díaz, Albert Ruiz and Antonio Viruel PDF

Trans. Amer. Math. Soc. 359 (2007), 1725-1764 Request permission

Abstract:

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

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