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Classification of finite simple groups — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T13:42:52.892Z
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Classification of finite simple groups — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_3f79ffdbdd3a (Metraipolis archive dc_3f79ffdbdd3a, sha256 a82c55b9ec4fec0dfb75fbdd38043b27659ef1201d38fa4f20a895c27dec12fd)

BibTeX

@misc{dc3f79ffdbdd3a,
  title = {Classification of finite simple groups — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_3f79ffdbdd3a; sha256 a82c55b9ec4fec0dfb75fbdd38043b27659ef1201d38fa4f20a895c27dec12fd},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, the classification of finite simple groups (popularly called the enormous theorem) is a result of group theory stating that 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 (the Tits group is sometimes regarded as a sporadic group because it is not strictly a group of Lie type, in which case there would be 27 sporadic groups). The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Simple groups can be seen as the basic building blocks of all finite groups, reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extension problem does not have a unique solution. Daniel Gorenstein (1923–1992), Richard Lyons, and Ronald Solomon are gradually publishing a simplified and revised version of the proof.

Tema degli esploratori: storia e filosofia della scienza (deposito sistematico; categoria «History of mathematics»).
Fonte: Wikipedia in inglese, voce «Classification of finite simple groups» — https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups
Wikidata Q1340623: «theorem» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1340623
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1371729148, consultata il 2026-10-06T11:59:28.541Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 8f1bae5ab6cbcc188cce3fbeb8460128f4e73c71645e032609c087931be259bf