Gorenstein–Harada theorem

In mathematical finite group theory, the Gorenstein–Harada theorem, proved by Gorenstein and Harada (1973, 1974) in a 464 page paper, classifies the simple finite groups of sectional 2-rank at most 4. It is part of the classification of finite simple groups.

Finite simple groups of section 2 rank at least 5 have Sylow 2-subgroups with a self-centralizing normal subgroup of rank at least 3, which implies that they have to be of either component type or of characteristic 2 type. Therefore the Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two subcases.