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cyclic group

mathematical group that can be generated as the set of powers of a single element
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cyclic group

Summary

cyclic group has Wikipedia articles in 23 language editions, a strong signal of global cultural recognition.[1]

Key Facts

  • cyclic group is a type of abelian group[2].
  • cyclic group is a type of finitely generated group[3].
  • cyclic group's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/cyclic-groups[4].
  • cyclic group's has characteristic is recorded as rank of a group[5].
  • cyclic group's studied by is recorded as group theory[6].
  • cyclic group's disjoint union of is recorded as list of values as qualifiers[7].
  • cyclic group's maintained by WikiProject is recorded as WikiProject Mathematics[8].

Body

Definition and Type

Recorded subclass of include abelian group[2] and finitely generated group[3].

Why It Matters

cyclic group has Wikipedia articles in 23 language editions, a strong signal of global cultural recognition.[1] It is known by 6 alternative names across languages and contexts.[9]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . The Theory of Groups, Volume 1. wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.
  6. [7] ↑ . wikidata.org.
  7. [8] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikidata sitelinks. wikidata.org.
  2. [9] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). cyclic group. Retrieved April 10, 2026, from https://4ort.xyz/entity/cyclic-group
MLA “cyclic group.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/cyclic-group.
BibTeX @misc{4ortxyz_cyclic-group_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{cyclic group}}, year = {2026}, url = {https://4ort.xyz/entity/cyclic-group}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): cyclic group — https://4ort.xyz/entity/cyclic-group (retrieved 2026-04-10)

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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 2d ago · Mynus grey · 2026-07-02 view diff on Wikidata ↗
    Disjoint union of → list of values as qualifiers
    Subclass of → —
    P14534 → IsCyclic
    Maintained by wikiproject → WikiProject Mathematics
    + 4 other properties edited (see Wikidata diff for full list)
    "/* wbcreateclaim-create:1| */ [[Property:P14534]]: IsCyclic, #quickstatements; #temporary_batch_1783013068346"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.