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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:algebraic_geometry
algebraic number theory
cryptography
|
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gptkbp:centralTo
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gptkb:Galois_theory
|
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gptkbp:definedIn
|
finite field
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gptkbp:describes
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symmetries of roots of polynomials
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gptkbp:example
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gptkb:group_of_people
dihedral group
cyclic group
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gptkbp:field
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gptkb:Galois_theory
abstract algebra
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gptkbp:firstDefined
|
19th century
|
|
gptkbp:generalizes
|
gptkb:étale_fundamental_group
profinite group
|
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gptkbp:hasProperty
|
gptkb:group_of_people
group structure
acts on roots of polynomials
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Galois groups
|
|
gptkbp:namedAfter
|
gptkb:Évariste_Galois
|
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gptkbp:notation
|
gptkb:Gal(E/F)
|
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gptkbp:relatedTo
|
gptkb:Kronecker–Weber_theorem
gptkb:fundamental_theorem_of_Galois_theory
gptkb:inverse_Galois_problem
gptkb:fundamental_group_(algebraic_geometry)
normal subgroup
automorphism group
field extensions
normal extension
permutation group
quotient group
solvable group
transitive group action
field automorphism
irreducible polynomial
extension degree
fixed field
primitive element theorem
splitting field
|
|
gptkbp:studiedBy
|
gptkb:Évariste_Galois
gptkb:Emil_Artin
gptkb:Richard_Dedekind
gptkb:Émile_Picard
|
|
gptkbp:usedFor
|
classify field extensions
determine solvability by radicals
study polynomial equations
|
|
gptkbp:usedIn
|
solvability of polynomials
|
|
gptkbp:bfsParent
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gptkb:Langlands_correspondence
gptkb:Algebraic_number_theory
|
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gptkbp:bfsLayer
|
5
|