symmetric group S_4
E1487994
UNEXPLORED
The symmetric group S₄ is the group of all 24 permutations of four elements, a fundamental example in group theory and a key object in the study of symmetries in algebra and geometry.
All labels observed (1)
| Label | Occurrences |
|---|---|
| symmetric group S_4 canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T21494626 — 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: symmetric group S_4 Context triple: [Fermat surface, hasAutomorphismGroupContaining, symmetric group S_4]
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A.
symmetric group S5
The symmetric group S5 is the group of all permutations of five elements, a fundamental finite group of order 120 that plays a key role in group theory and Galois theory.
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B.
Coxeter group
A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
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C.
SL(2,7)
SL(2,7) is the special linear group of 2×2 matrices with determinant 1 over the finite field with 7 elements, a non-abelian finite group of order 336 that plays an important role in group theory and geometry.
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D.
Schreier
Schreier is a surname of Germanic origin borne by various notable individuals, including mathematicians and other professionals.
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E.
Burnside's lemma
Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
- 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: symmetric group S_4 Target entity description: The symmetric group S₄ is the group of all 24 permutations of four elements, a fundamental example in group theory and a key object in the study of symmetries in algebra and geometry.
-
A.
symmetric group S5
The symmetric group S5 is the group of all permutations of five elements, a fundamental finite group of order 120 that plays a key role in group theory and Galois theory.
-
B.
Coxeter group
A Coxeter group is an abstract group generated by reflections across hyperplanes, fundamental in the classification and study of regular polytopes, tessellations, and symmetries in geometry and algebra.
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C.
SL(2,7)
SL(2,7) is the special linear group of 2×2 matrices with determinant 1 over the finite field with 7 elements, a non-abelian finite group of order 336 that plays an important role in group theory and geometry.
-
D.
Schreier
Schreier is a surname of Germanic origin borne by various notable individuals, including mathematicians and other professionals.
-
E.
Burnside's lemma
Burnside's lemma is a result in group theory and combinatorics that counts distinct configurations under symmetries by averaging the number of fixed points of group actions.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.