"cycle group" meaning in English

{
  "forms": [
    {
      "form": "kth cycle group",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "cycle groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "kth cycle group"
      },
      "expansion": "kth cycle group (plural cycle 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": "Algebraic topology",
          "orig": "en:Algebraic topology",
          "parents": [
            "Algebra",
            "Topology",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The kernel of the kᵗʰ boundary homomorphism (of a given chain complex)."
      ],
      "id": "en-cycle_group-en-noun-om-n5YUr",
      "links": [
        [
          "algebraic topology",
          "algebraic topology"
        ],
        [
          "kernel",
          "kernel"
        ],
        [
          "boundary homomorphism",
          "boundary homomorphism"
        ],
        [
          "chain complex",
          "chain complex"
        ]
      ],
      "raw_glosses": [
        "(algebraic topology) The kernel of the kᵗʰ boundary homomorphism (of a given chain complex)."
      ],
      "topics": [
        "algebraic-topology",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "cycle group"
}

{
  "forms": [
    {
      "form": "kth cycle group",
      "tags": [
        "canonical"
      ]
    },
    {
      "form": "cycle groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "kth cycle group"
      },
      "expansion": "kth cycle group (plural cycle 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:Algebraic topology"
      ],
      "glosses": [
        "The kernel of the kᵗʰ boundary homomorphism (of a given chain complex)."
      ],
      "links": [
        [
          "algebraic topology",
          "algebraic topology"
        ],
        [
          "kernel",
          "kernel"
        ],
        [
          "boundary homomorphism",
          "boundary homomorphism"
        ],
        [
          "chain complex",
          "chain complex"
        ]
      ],
      "raw_glosses": [
        "(algebraic topology) The kernel of the kᵗʰ boundary homomorphism (of a given chain complex)."
      ],
      "topics": [
        "algebraic-topology",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "cycle group"
}