# Classification of finite simple groups

- kind: problem
- status: solved (evidence tier V3)
- year: 1892

**Statement.** Every finite simple group is cyclic, alternating, of Lie type, or one of 26 sporadic groups.

The proof spans tens of thousands of pages by more than a hundred authors over fifty years. A 'second generation' proof, begun by Gorenstein, Lyons and Solomon, is still being written up to make it checkable by one person. It is the strongest argument for formal verification at scale.

*Evidence tier V3 is the import default for a result the curation records as settled in the published record. No formal proof or certificate is attached to this page yet.*

Closed 1983 announced; 2004 gaps closed (Aschbacher and Smith).

## Sources

- [Wikipedia: Classification of finite simple groups](https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups)

[Algebra and groups](/wiki/Space:algebra.md) · [Mathematics](/wiki/Continent:mathematics.md)

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