{
  "schema": "groups.qft.org/entity/2",
  "versions": {
    "schema": "2.0.0",
    "dataset": "2026.11-workbench.4",
    "application": "6.0.0",
    "algorithm": "groups-workbench-4.0.0",
    "released": "2026-11-08"
  },
  "canonicalURL": "https://groups.qft.org/atlas/families/finite-f4/",
  "entity": {
    "id": "family:finite-f4",
    "slug": "finite-f4",
    "name": "Finite simple groups of type F₄",
    "symbol": "F₄(q)",
    "category": "finite",
    "level": "classification",
    "aliases": [],
    "searchTerms": [
      "Finite simple groups of type F₄",
      "F₄(q)"
    ],
    "tags": [
      "Finite simple classification"
    ],
    "summary": "All prime powers q ≥ 2; take the simple central quotient.",
    "definition": "The untwisted Chevalley finite group of Lie type F₄, in its simple central-quotient form.",
    "definitionEvidence": [
      {
        "source": "finite-wilson-exceptional",
        "locator": "Ten exceptional families"
      }
    ],
    "properties": [
      {
        "key": "parameters",
        "label": "Parameter domain",
        "value": "q: q = p^f, with p prime and f ≥ 1",
        "evidence": [
          {
            "source": "finite-wilson-exceptional",
            "locator": "Ten exceptional families"
          }
        ],
        "assumptions": []
      },
      {
        "key": "restriction",
        "label": "Scope and restrictions",
        "value": "All prime powers q ≥ 2; take the simple central quotient.",
        "evidence": [
          {
            "source": "finite-wilson-exceptional",
            "locator": "Ten exceptional families"
          }
        ],
        "assumptions": []
      }
    ],
    "sections": [
      {
        "id": "conventions",
        "title": "Conventions and use",
        "paragraphs": [
          {
            "text": "The finite-field object is distinct from a compact or complex Lie group with the same root-system label.",
            "evidence": [
              {
                "source": "finite-gap-groups",
                "locator": "IsomorphismTypeInfoFiniteSimpleGroup; SimpleGroup"
              }
            ],
            "assumptions": []
          }
        ]
      }
    ],
    "relationships": [],
    "capabilities": [],
    "kind": "family",
    "data": {
      "parameters": [
        {
          "name": "q",
          "domain": "q = p^f, with p prime and f ≥ 1"
        }
      ],
      "exceptions": [],
      "scope": "All prime powers q ≥ 2; take the simple central quotient."
    }
  },
  "claims": [
    {
      "id": "family:finite-f4#definition",
      "subject": "family:finite-f4",
      "key": "definition",
      "label": "Definition",
      "value": "The untwisted Chevalley finite group of Lie type F₄, in its simple central-quotient form.",
      "evidence": [
        {
          "source": "finite-wilson-exceptional",
          "locator": "Ten exceptional families"
        }
      ],
      "assumptions": [],
      "reviewStatus": "pending-expert-review",
      "revision": "2026.11-workbench.4"
    },
    {
      "id": "family:finite-f4#parameters",
      "subject": "family:finite-f4",
      "key": "parameters",
      "label": "Parameter domain",
      "value": "q: q = p^f, with p prime and f ≥ 1",
      "evidence": [
        {
          "source": "finite-wilson-exceptional",
          "locator": "Ten exceptional families"
        }
      ],
      "assumptions": [],
      "reviewStatus": "pending-expert-review",
      "revision": "2026.11-workbench.4"
    },
    {
      "id": "family:finite-f4#restriction",
      "subject": "family:finite-f4",
      "key": "restriction",
      "label": "Scope and restrictions",
      "value": "All prime powers q ≥ 2; take the simple central quotient.",
      "evidence": [
        {
          "source": "finite-wilson-exceptional",
          "locator": "Ten exceptional families"
        }
      ],
      "assumptions": [],
      "reviewStatus": "pending-expert-review",
      "revision": "2026.11-workbench.4"
    },
    {
      "id": "family:finite-f4#conventions-1",
      "subject": "family:finite-f4",
      "key": "conventions-1",
      "label": "Conventions and use",
      "value": "The finite-field object is distinct from a compact or complex Lie group with the same root-system label.",
      "evidence": [
        {
          "source": "finite-gap-groups",
          "locator": "IsomorphismTypeInfoFiniteSimpleGroup; SimpleGroup"
        }
      ],
      "assumptions": [],
      "reviewStatus": "pending-expert-review",
      "revision": "2026.11-workbench.4"
    }
  ],
  "sources": [
    {
      "id": "finite-wilson-exceptional",
      "title": "Finite simple groups: Lecture 4 — Exceptional groups",
      "authors": [
        "Robert A. Wilson"
      ],
      "url": "https://webspace.maths.qmul.ac.uk/r.a.wilson/FSG/lect4.pdf",
      "kind": "lecture-notes",
      "locatorHint": "Ten exceptional families; Suzuki–Ree parameters and small cases; G2",
      "licenseNote": "Linked for verification. No redistribution licence is asserted; this dataset contains original summaries and selected mathematical facts, not source tables."
    },
    {
      "id": "finite-gap-groups",
      "title": "GAP Reference Manual: Groups",
      "authors": [
        "The GAP Group"
      ],
      "url": "https://gap-system.github.io/gap/doc/ref/chap39_mj.html",
      "kind": "documentation",
      "locatorHint": "IsSimpleGroup; IsomorphismTypeInfoFiniteSimpleGroup; SimpleGroup",
      "licenseNote": "Linked for verification. No redistribution licence is asserted; this dataset contains original summaries and selected mathematical facts, not source tables."
    }
  ],
  "review": {
    "status": "pending-expert-review",
    "label": "Expert review pending",
    "currentReviews": 0,
    "staleReviews": 0,
    "fingerprint": "7df7b2b311e2f7e97a98baf561231a03e85121289d4ccb29899a413a24f8e0a9",
    "reviewers": []
  }
}