{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:e5df3ee6-ad9c-4544-bf44-ea5c27385154",
  "labels": {
    "zh-CN": "中心",
    "en": "centre"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "f1220e1bec6390637ca4952be6cf685fc5200419787c07e8ec3c51b70ed3a910",
  "occurrences": [
    {
      "concept_id": "urn:uuid:e5df3ee6-ad9c-4544-bf44-ea5c27385154",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-02/05-normal-subgroups-and-factor-groups",
      "anchor": "concept-2-centre",
      "chapter": "2",
      "section": "2.5",
      "offset": 3688,
      "range": [
        8410,
        8626
      ],
      "source_revision": "fee321b0500c365016e4a1e97ab854a0117b68f310294f13cc853414839be4d8",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "中心(centre)",
      "context": {
        "range": [
          8327,
          9180
        ],
        "quote": "> [!example] <a class=\"object-permalink\" href=\"#example-2-20\">例 2.20</a> \n>\n> 群$G$的<u id=\"concept-2-centre\" class=\"concept-term\" data-concept-identity=\"urn:uuid:e5df3ee6-ad9c-4544-bf44-ea5c27385154\" data-concept-route=\"/concept-identities#concept-e5df3ee6-ad9c-4544-bf44-ea5c27385154\">中心(centre)</u>$Z$被定义为与$G$的所有元素都相互满足交换律的元素集合\n>\n> $$\n> Z=\\{z \\in G \\mid z g=g z \\text {对于全体 } g \\in G\\}\n> $$\n>\n> 这个集合构成了$G$的子群，因为三个基本要求都成立：\n>\n> 封闭性：如果$z, z^{\\prime} \\in Z$，那么$z z^{\\prime} \\in Z$，因为\n>\n> $$\n> \\left(z z^{\\prime}\\right) g=z\\left(z^{\\prime} g\\right)=z\\left(g z^{\\prime}\\right)=(z g) z^{\\prime}=(g z) z^{\\prime}=g\\left(z z^{\\prime}\\right) \\text {. }\n> $$\n>\n> 单位元：$e \\in Z$，因为对于所有$g \\in G$，$e g=g e=g$。\n>\n> 逆元：如果$z \\in Z$，那么$z^{-1} \\in Z$，因为\n>\n> $$\n> z^{-1} g=z^{-1} g e=z^{-1} g z z^{-1}=z^{-1} z g z^{-1}=g z^{-1}\n> $$\n>\n> 由于对于所有$g \\in G$，$g Z=Z g$，这个子群显是正规的",
        "quote_sha256": "384556700c7f471c290b96e2dd98887fb652a3a854bd522b0c6536316d98d6bd",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-02/05-normal-subgroups-and-factor-groups",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-160800f4b6c4ef88b0450e5c"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-02/05-normal-subgroups-and-factor-groups",
      "lang": "zh-CN",
      "section": "2.5",
      "signal": "term-mark",
      "label": "中心",
      "english": "centre",
      "offset": 3078
    }
  ],
  "statements": [],
  "resolved_references": [
    {
      "raw": "href=\"#example-2-20\"",
      "href": "#example-2-20",
      "range": [
        8368,
        8388
      ],
      "relation": "references",
      "target_route": "zh/chapter-02/05-normal-subgroups-and-factor-groups",
      "target_anchor": "example-2-20",
      "resolved": true,
      "reason": null,
      "source_revision": "fee321b0500c365016e4a1e97ab854a0117b68f310294f13cc853414839be4d8",
      "source_route": "zh/chapter-02/05-normal-subgroups-and-factor-groups",
      "occurrence_id": "occ-160800f4b6c4ef88b0450e5c"
    }
  ],
  "reading_order": [
    "occ-160800f4b6c4ef88b0450e5c"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "52d4740e7fb067f4091d54c7dedef04f05bb7be4f736314eb7687cda4014d37f",
  "optional_enrichments": []
}