In mathematical finite group theory, the Gorenstein–Harada theorem, proved by 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

Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below. These groups can be seen as the basic building blocks of all finite groups, in much the same way as the prime numbers are the basic...

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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

Characteristic 2 type

In mathematical finite group theory, a group is said to be of characteristic 2 type or even type or of even characteristic if it resembles a group of Lie type over a field of characteristic 2....

. Therefore the Gorenstein–Harada theorem splits the problem of classifying finite simple groups into these two subcases.