Galois group of the rationals

URI: https://gptkb.org/entity/Galois_group_of_the_rationals
GPTKB entity
Statements (26)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkbp:actsOn algebraic numbers
roots of polynomials with rational coefficients
gptkbp:algebraicClosure \\overline{\\mathbb{Q}}
gptkbp:alsoKnownAs gptkb:absolute_Galois_group_of_Q
gptkbp:category gptkb:Galois_theory
group theory
gptkbp:contains all finite Galois groups over Q
gptkbp:defines group of field automorphisms of the algebraic closure of Q that fix Q
gptkbp:field rational numbers
gptkbp:hasSubgroup gptkb:Galois_group_of_finite_extensions_of_Q
gptkb:Galois_group_of_the_reals
https://www.w3.org/2000/01/rdf-schema#label Galois group of the rationals
gptkbp:importantFor gptkb:Langlands_program
algebraic number theory
arithmetic geometry
class field theory
gptkbp:openProblem explicit description of its structure
gptkbp:relatedTo gptkb:Kronecker–Weber_theorem
gptkb:inverse_Galois_problem
gptkb:Grothendieck's_theory_of_dessins_d'enfants
gptkbp:structure profinite group
gptkbp:symbol Gal(\\overline{\\mathbb{Q}}/\\mathbb{Q})
gptkbp:topology profinite topology
gptkbp:bfsParent gptkb:dessins_d'enfants
gptkbp:bfsLayer 6