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    "name": "Minus-type even orthogonal finite simple groups",
    "symbol": "PΩ⁻(2n,q)",
    "category": "finite",
    "level": "classification",
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      "O₂ₙ⁻(q)"
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    "tags": [
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    ],
    "summary": "n ≥ 4; minus type has Witt index n−1.",
    "definition": "The projective Ω group of a nonsplit nondegenerate quadratic form on Fq^(2n).",
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        "paragraphs": [
          {
            "text": "dimension 4: PΩ⁻(4,q) ≅ PSL(2,q²); use the linear family.",
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            "text": "dimension 6: PΩ⁻(6,q) ≅ PSU(4,q); use the unitary family.",
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                "locator": "Small-dimensional orthogonal groups"
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          "at": "dimension 4",
          "description": "PΩ⁻(4,q) ≅ PSL(2,q²); use the linear family."
        },
        {
          "at": "dimension 6",
          "description": "PΩ⁻(6,q) ≅ PSU(4,q); use the unitary family."
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      "value": "n ≥ 4; minus type has Witt index n−1.",
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      "id": "family:finite-even-orthogonal-minus#exceptions-1",
      "subject": "family:finite-even-orthogonal-minus",
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      "label": "Exceptions and identifications",
      "value": "dimension 4: PΩ⁻(4,q) ≅ PSL(2,q²); use the linear family.",
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      "key": "exceptions-2",
      "label": "Exceptions and identifications",
      "value": "dimension 6: PΩ⁻(6,q) ≅ PSU(4,q); use the unitary family.",
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          "source": "finite-wilson-classical",
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      "assumptions": [],
      "reviewStatus": "pending-expert-review",
      "revision": "2026.11-workbench.4"
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  "sources": [
    {
      "id": "finite-wilson-classical",
      "title": "Finite simple groups: Lecture 3 — Classical groups",
      "authors": [
        "Robert A. Wilson"
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      "kind": "lecture-notes",
      "locatorHint": "Symplectic, unitary and orthogonal groups",
      "licenseNote": "Linked for verification. No redistribution licence is asserted; this dataset contains original summaries and selected mathematical facts, not source tables."
    },
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      "id": "finite-wilson-classical-notes",
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      "authors": [
        "Robert A. Wilson"
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      "kind": "lecture-notes",
      "locatorHint": "Sections 3.2–3.5",
      "licenseNote": "Linked for verification. No redistribution licence is asserted; this dataset contains original summaries and selected mathematical facts, not source tables."
    }
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