In mathematical

finite Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marke ...

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

, the Gorenstein–Harada theorem, proved by in a 464-page paper,"Abc conjecture — The Enormity of Math"
''Medium'', Cami Rosso, Feb 23, 2017 classifies the simple finite groups of sectional 2-rank at most 4. It is part of the

classification of finite simple groups In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else i ...

. Finite simple groups of section 2 that rank at least 5, have

Sylow 2-subgroup In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed ...

s 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 sub-cases.

References

* * Theorems about finite groups {{algebra-stub