"lamplighter group" meaning in English

{
  "etymology_text": "The group can be viewed as acting on a doubly infinite sequence of street lamps …,l_-2,l_-1,l_0,l_1,l_2,l_3,… each of which may be on or off, with a lamplighter standing at some lamp l_k.",
  "forms": [
    {
      "form": "lamplighter groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lamplighter group (plural lamplighter groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The restricted wreath product mathbf Z₂≀ mathbf Z."
      ],
      "id": "en-lamplighter_group-en-noun-QCHzE~RD",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "wreath product",
          "wreath product"
        ]
      ],
      "raw_glosses": [
        "(group theory) The restricted wreath product mathbf Z₂≀ mathbf Z."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "lamplighter group"
      ]
    }
  ],
  "word": "lamplighter group"
}

{
  "etymology_text": "The group can be viewed as acting on a doubly infinite sequence of street lamps …,l_-2,l_-1,l_0,l_1,l_2,l_3,… each of which may be on or off, with a lamplighter standing at some lamp l_k.",
  "forms": [
    {
      "form": "lamplighter groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "lamplighter group (plural lamplighter groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Group theory"
      ],
      "glosses": [
        "The restricted wreath product mathbf Z₂≀ mathbf Z."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "wreath product",
          "wreath product"
        ]
      ],
      "raw_glosses": [
        "(group theory) The restricted wreath product mathbf Z₂≀ mathbf Z."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "lamplighter group"
      ]
    }
  ],
  "word": "lamplighter group"
}