group

algebraic set with an invertible, associative internal operation admitting a neutral element
Intangible mathematical_concept Q83478
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group

Summary

group is a mathematical concept[1]. group ranks in the top 2% of mathematical_concept entities by monthly Wikipedia readership (834 views/month).[2]

Key Facts

  • group's image is recorded as Rubiks revenge tilt.jpg[3].
  • group's instance of is recorded as mathematical concept[4].
  • group's GND ID is recorded as 4022379-6[5].
  • group's subclass of is recorded as monoid[6].
  • group's subclass of is recorded as inverse semigroup[7].
  • group's subclass of is recorded as Moufang loop[8].
  • group's subclass of is recorded as groupoid[9].
  • group's subclass of is recorded as epigroup[10].
  • group's subclass of is recorded as algebraic structure[11].
  • group's subclass of is recorded as group object[12].
  • group's subclass of is recorded as loop[13].
  • group's Commons category is recorded as Group theory[14].
  • group's BNCF Thesaurus ID is recorded as 5497[15].
  • group's has part is recorded as set[16].
  • group's has part is recorded as binary operation[17].
  • group's has part is recorded as identity element[18].
  • group's has part is recorded as inverse[19].
  • group's Freebase ID is recorded as /m/04xl4[20].
  • group's NL CR AUT ID is recorded as ph180740[21].
  • group's topic's main category is recorded as Q13324638[22].
  • group's Dewey Decimal Classification is recorded as 512.2[23].
  • group's Gran Enciclopèdia Catalana ID is recorded as 0157361[24].
  • group's Encyclopædia Britannica Online ID is recorded as topic/group-mathematics[25].
  • group's topic has template is recorded as Template:Group navbox[26].
  • group's has characteristic is recorded as closure[27].

Why It Matters

group ranks in the top 2% of mathematical_concept entities by monthly Wikipedia readership (834 views/month).[2] group has Wikipedia articles in 30 language editions, a strong signal of global cultural recognition.[28] group is known by 15 alternative names across languages and contexts.[29]

References

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

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . wikidata.org.
  14. [16] . wikidata.org.
  15. [17] . wikidata.org.
  16. [18] . wikidata.org.
  17. [19] . wikidata.org.
  18. [20] . Freebase Data Dumps. wikidata.org.
  19. [21] . wikidata.org.
  20. [22] . wikidata.org.
  21. [23] . Nuovo soggettario. Retrieved . wikidata.org.
  22. [24] . wikidata.org.
  23. [25] . wikidata.org.
  24. [26] . wikidata.org.
  25. [27] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [28] . Wikidata sitelinks. wikidata.org.
  3. [29] . 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). group. Retrieved May 3, 2026, from https://4ort.xyz/entity/group
MLA “group.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/group.
BibTeX @misc{4ortxyz_group_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{group}}, year = {2026}, url = {https://4ort.xyz/entity/group}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): group — https://4ort.xyz/entity/group (retrieved 2026-05-03)

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