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group action

operation of the elements of a group as transformations or automorphisms (mathematics)
Thing general Q288465
group action
Incnis Mrsi · Public Domain · Wikimedia
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group action

Summary

group action ranks in the top 2% of general entities by monthly Wikipedia readership (1,451 views/month).[1]

Key Facts

  • group action is a type of homomorphism[2].
  • group action is a type of binary operation[3].
  • group action is a type of partial group action on a set[4].
  • group action is a type of Semigroup action[5].
  • group action is part of group theory[6].
  • group action's Commons category is recorded as Group actions[7].
  • group action's topic's main category is recorded as Category:Group actions[8].
  • group action's Stack Exchange tag is recorded as https://math.stackexchange.com/tags/group-actions[9].
  • group action's Stack Exchange tag is recorded as https://mathoverflow.net/tags/group-actions[10].
  • group action's different from is recorded as group operation[11].
  • group action's maintained by WikiProject is recorded as WikiProject Mathematics[12].

Body

Definition and Type

Recorded subclass of include homomorphism[2], binary operation[3], partial group action on a set[4], and Semigroup action[5].

Use and Application

group action is part of group theory[6].

Why It Matters

group action ranks in the top 2% of general entities by monthly Wikipedia readership (1,451 views/month).[1] It has Wikipedia articles in 20 language editions, a strong signal of global cultural recognition.[13] It is known by 10 alternative names across languages and contexts.[14]

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.
  8. [9] ↑ . wikidata.org.
  9. [10] ↑ . wikidata.org.
  10. [11] ↑ . wikidata.org.
  11. [12] ↑ . wikidata.org.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [13] ↑ . Wikidata sitelinks. wikidata.org.
  3. [14] ↑ . 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 action. Retrieved April 10, 2026, from https://4ort.xyz/entity/group-action
MLA “group action.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/group-action.
BibTeX @misc{4ortxyz_group-action_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{group action}}, year = {2026}, url = {https://4ort.xyz/entity/group-action}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): group action — https://4ort.xyz/entity/group-action (retrieved 2026-04-10)

Canonical URL: https://4ort.xyz/entity/group-action · Last refreshed:

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. 1d ago · Charp238 · 2026-05-20 view diff on Wikidata ↗
    Part of → —
    Subclass of → homomorphism, binary operation, partial group action on a set +1
    Part of → group theory
    Topic's main category → Category:Group actions
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P8417]]: Group_action"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.