Theory of Groups
E437488
Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Theory of Groups canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4416537 — 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: Theory of Groups Context triple: [Marshall Hall, notableWork, Theory of Groups]
-
A.
Gruppentheorie und Quantenmechanik
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
-
B.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
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C.
Lie theory
Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
-
D.
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.
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E.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
- 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: Theory of Groups Target entity description: Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
-
A.
Gruppentheorie und Quantenmechanik
Gruppentheorie und Quantenmechanik is Hermann Weyl’s influential 1928 monograph that systematically applies group theory to the foundations of quantum mechanics, shaping the mathematical formulation of modern physics.
-
B.
Abelian groups
Abelian groups are algebraic structures in which the group operation is commutative, meaning the order of combining elements does not affect the result.
-
C.
Lie theory
Lie theory is a branch of mathematics that studies continuous symmetry through Lie groups and Lie algebras, with deep applications in geometry, analysis, and theoretical physics.
-
D.
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.
-
E.
Methods of Representation Theory
Methods of Representation Theory is a foundational multi-volume work in mathematics that systematically develops the theory of group and algebra representations, coauthored by Israel Gelfand and collaborators.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
abstract algebra textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| educationalLevel | advanced ⓘ |
| field |
abstract algebra
ⓘ
mathematics ⓘ |
| focusesOn | systematic development of group theory ⓘ |
| hasGenre |
academic textbook
ⓘ
nonfiction ⓘ |
| intendedAudience |
mathematics students
ⓘ
research mathematicians ⓘ |
| language | English ⓘ |
| mainSubject | group theory ⓘ |
| structure | rigorous exposition ⓘ |
| topic |
Sylow theorems
NERFINISHED
ⓘ
cosets ⓘ finite groups ⓘ group actions ⓘ group representations ⓘ groups ⓘ homomorphisms ⓘ infinite groups ⓘ isomorphism theorems ⓘ normal subgroups ⓘ permutation groups ⓘ quotient groups ⓘ subgroups ⓘ |
| usedFor |
advanced mathematical study
ⓘ
mathematical research ⓘ |
| usedIn |
advanced undergraduate courses in algebra
ⓘ
graduate courses in 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: Theory of Groups Description of subject: Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.