Theorem

Classification of Finite Simple Groups

Algebra

Every finite simple group belongs to one of a small number of known infinite families, or is one of 26 sporadic exceptions. The result of a collaborative proof effort spanning decades and many hundreds of journal articles by numerous mathematicians, it is among the largest theorems ever proved.

Facts

Statement

Every finite simple group is isomorphic to a cyclic group of prime order, an alternating group of degree five or more, a group of Lie type, or one of twenty-six sporadic exceptions falling outside those infinite families. 1

Proof Year

1983 1

Gorenstein announced the classification complete in 1983; a gap in the quasithin case was not fully closed until Aschbacher and Smith published a 1221-page proof in 2004.

Classification

Statement Form

Classification Theorem 1

Connections

Associated With

Feit-Thompson Theorem

Jordan-Holder Theorem

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Classification Theorem

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Algebra

Sources

1. Classification of Finite Simple Groups (Wikipedia)

Wikipedia

Introduction, first paragraph
every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic
History of the proof section, 1983 announcement
Daniel Gorenstein announced in 1983 that the finite simple groups had all been classified

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Classification of Finite Simple Groups

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