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Hopfian group

group for which every surjective endomorphism is bijective
Thing general Q5900529
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Hopfian group

Summary

Hopfian group ranks in the top 2% of general entities by monthly Wikipedia readership (53 views/month).[1]

Key Facts

  • Hopfian group is credited with the discovery of Heinz Hopf[2].
  • Heinz Hopf is named after Hopfian group[3].
  • Hopfian group is a type of group[4].

Body

Definition and Type

Hopfian group is a type of group[4].

Origins

Heinz Hopf is named after Hopfian group[3].

Why It Matters

Hopfian group ranks in the top 2% of general entities by monthly Wikipedia readership (53 views/month).[1] It has Wikipedia articles in 7 language editions, a strong signal of global cultural recognition.[5]

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.

Aggregate / graph-position facts

  1. [1] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [5] ↑ . 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). Hopfian group. Retrieved April 10, 2026, from https://4ort.xyz/entity/hopfian-group
MLA “Hopfian group.” 4ort.xyz Knowledge Graph, 4ort.xyz, 10 Apr. 2026, https://4ort.xyz/entity/hopfian-group.
BibTeX @misc{4ortxyz_hopfian-group_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Hopfian group}}, year = {2026}, url = {https://4ort.xyz/entity/hopfian-group}, note = {Accessed: 2026-04-10}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Hopfian group — https://4ort.xyz/entity/hopfian-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. 4w ago · MsynBot bot · 2026-06-20 view diff on Wikidata ↗
    Subclass of → group
    Subclass of → —
    Named after → Heinz Hopf
    Aliases → —
    + 2 other properties edited (see Wikidata diff for full list)
    "/* wbeditentity-update:0| */ add badge [[Q70893996]] to kowiki sitelink; see [[Wikidata:Sitelinks to redirects]] for details #msynbotTask10"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.