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free group

free object in the category of groups; a group admitting a presentation without any relations
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free group

Summary

free group has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[1]

Key Facts

  • free group is a type of Artin group[2].
  • free group is a type of free object[3].
  • free group is a type of residually finite group[4].
  • free group's Commons category is recorded as Free groups[5].
  • free group's Stack Exchange tag is recorded as https://mathoverflow.net/tags/free-groups[6].
  • free group's different from is recorded as free abelian group[7].
  • free group's studied by is recorded as group theory[8].

Body

Definition and Type

Recorded subclass of include Artin group[2], free object[3], and residually finite group[4].

Why It Matters

free group has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[1]

References

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

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . 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.

📑 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). free group. Retrieved April 10, 2026, from https://4ort.xyz/entity/free-group
MLA “free group.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/free-group.
BibTeX @misc{4ortxyz_free-group_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{free group}}, year = {2026}, url = {https://4ort.xyz/entity/free-group}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): free group — https://4ort.xyz/entity/free-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. 3d ago · Mynus grey · 2026-07-02 view diff on Wikidata ↗
    Subclass of → —
    Different from → free abelian group
    P14534 → FreeGroup
    Aliases → —
    + 2 other properties edited (see Wikidata diff for full list)
    "/* wbcreateclaim-create:1| */ [[Property:P14534]]: FreeGroup, #quickstatements; #temporary_batch_1783013068346"
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