absolute Galois group of the rational numbers

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Weyl_group
gptkbp:actsOn	algebraic numbers
gptkbp:alsoKnownAs	Galois group of Q
gptkbp:category	algebraic number theory field theory group theory
gptkbp:contains	Galois group of finite extensions of ℚ
gptkbp:defines	the Galois group of the field extension of the algebraic closure of the rationals over the rationals
gptkbp:fieldExtension	ℚ̄/ℚ
https://www.w3.org/2000/01/rdf-schema#label	absolute Galois group of the rational numbers
gptkbp:importantFor	gptkb:algebraic_geometry number theory arithmetic geometry
gptkbp:property	non-abelian every finite group is a quotient of a closed subgroup topologically finitely generated universal for finite Galois extensions of ℚ unknown explicit structure
gptkbp:relatedTo	gptkb:Langlands_program gptkb:étale_fundamental_group gptkb:Kronecker–Weber_theorem gptkb:inverse_Galois_problem gptkb:Artin_reciprocity gptkb:Grothendieck's_anabelian_geometry class field theory
gptkbp:structure	profinite group
gptkbp:studiedBy	gptkb:Jean-Pierre_Serre gptkb:John_Tate gptkb:Alexander_Grothendieck gptkb:Gerd_Faltings
gptkbp:symbol	gptkb:Gal(ℚ̄/ℚ)
gptkbp:bfsParent	gptkb:étale_fundamental_group
gptkbp:bfsLayer	7