Theorie der Gruppen von endlicher Ordnung
E599907
"Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
All labels observed (3)
How this entity was disambiguated
This entity first appeared as the object of triple T6624423 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Theorie der Gruppen von endlicher Ordnung Context triple: [Andreas Speiser, notableWork, Theorie der Gruppen von endlicher Ordnung]
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A.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
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B.
Moderne Algebra
Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
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C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
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D.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
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E.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Theorie der Gruppen von endlicher Ordnung Target entity description: "Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
-
A.
Theorie der Transformationsgruppen
Theorie der Transformationsgruppen is Sophus Lie’s foundational multi-volume work that established the theory of continuous transformation groups, now known as Lie groups, and their applications to differential equations and geometry.
-
B.
Moderne Algebra
Moderne Algebra is a foundational 20th-century textbook that systematically developed abstract algebra and helped shape the modern axiomatic approach to the subject.
-
C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
D.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
-
E.
Noether's isomorphism theorems
Noether's isomorphism theorems are fundamental results in abstract algebra that relate quotient structures and substructures of groups, rings, and modules, providing a unifying framework for understanding homomorphic images and factor structures.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ work on finite group theory ⓘ |
| author | Otto Hölder NERFINISHED ⓘ |
| citedAs | foundational work in finite group theory ⓘ |
| contributionTo |
development of finite group theory
ⓘ
foundations of abstract algebra ⓘ |
| field |
abstract algebra
ⓘ
group theory ⓘ |
| genre | research monograph ⓘ |
| hasNotableConcept |
Hölder program for classification of finite groups
ⓘ
use of composition series in group classification ⓘ |
| historicalSignificance |
early systematic exposition of finite group theory
ⓘ
helped shape modern axiomatic approach to groups ⓘ |
| influenced |
20th-century algebraists
ⓘ
modern treatments of group theory ⓘ |
| intendedAudience |
advanced students of mathematics
ⓘ
mathematicians ⓘ |
| language | German NERFINISHED ⓘ |
| titleLanguage | German ⓘ |
| titleTranslation | Theory of Groups of Finite Order NERFINISHED ⓘ |
| topic |
composition series
ⓘ
finite groups ⓘ group homomorphisms ⓘ group structure ⓘ normal subgroups ⓘ quotient groups ⓘ simple groups ⓘ subgroups ⓘ |
| usedIn | historical studies of algebra ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Theorie der Gruppen von endlicher Ordnung Description of subject: "Theorie der Gruppen von endlicher Ordnung" is a foundational mathematical monograph on finite group theory that helped shape the modern development of abstract algebra.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Die Theorie der Gruppen von endlicher Ordnung
this entity surface form:
Die Theorie der Gruppen von endlicher Ordnung mit Anwendungen auf algebraische Zahlentheorie