Galois group of the rationals

GPTKB entity

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
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	gptkb:profinite_group
gptkbp:symbol	gptkb:Gal(\overline{\mathbb{Q}}/\mathbb{Q})
gptkbp:topology	profinite topology
gptkbp:bfsParent	gptkb:dessins_d'enfants
gptkbp:bfsLayer	6
http://www.w3.org/2000/01/rdf-schema#label	Galois group of the rationals