Burnside's problem
E1434455
UNEXPLORED
Burnside's problem is a famous question in group theory asking whether a finitely generated group in which every element has finite order must necessarily be finite.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Burnside's problem canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T20505622 — 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: Burnside's problem Context triple: [William Burnside, knownFor, Burnside's problem]
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A.
Feit–Thompson theorem
The Feit–Thompson theorem is a landmark result in group theory that proves every finite group of odd order is solvable, marking the first major classification of a broad class of finite simple groups.
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B.
Zassenhaus conjecture
The Zassenhaus conjecture is a prominent open problem in group theory concerning the structure of units in integral group rings and their relation to the underlying finite group.
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C.
Hilbert’s second problem
Hilbert’s second problem is one of David Hilbert’s famous list of 23 problems, asking for a proof of the consistency of arithmetic from a finite set of axioms using finitary methods.
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D.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
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E.
Hilbert's first problem
Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.
- 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: Burnside's problem Target entity description: Burnside's problem is a famous question in group theory asking whether a finitely generated group in which every element has finite order must necessarily be finite.
-
A.
Feit–Thompson theorem
The Feit–Thompson theorem is a landmark result in group theory that proves every finite group of odd order is solvable, marking the first major classification of a broad class of finite simple groups.
-
B.
Zassenhaus conjecture
The Zassenhaus conjecture is a prominent open problem in group theory concerning the structure of units in integral group rings and their relation to the underlying finite group.
-
C.
Hilbert’s second problem
Hilbert’s second problem is one of David Hilbert’s famous list of 23 problems, asking for a proof of the consistency of arithmetic from a finite set of axioms using finitary methods.
-
D.
Hilbert’s twenty-third problem
Hilbert’s twenty-third problem is one of David Hilbert’s famous list of unsolved problems, focusing on the further development and systematic application of the calculus of variations.
-
E.
Hilbert's first problem
Hilbert's first problem is one of David Hilbert’s famous list of 23 problems, asking whether there exists a set whose size is strictly between that of the integers and the real numbers, i.e., the status of the continuum hypothesis.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.