inverse Galois problem over the rationals
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:asks_whether |
every finite group is the Galois group of some Galois extension of the rationals
|
| gptkbp:concerns |
gptkb:Galois_groups
field extensions |
| gptkbp:field |
gptkb:algebra
number theory |
| gptkbp:first_formulated |
19th century
|
| gptkbp:formulated_over |
rational numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
inverse Galois problem over the rationals
|
| gptkbp:notable_progress |
using generic polynomials
using rigidity method |
| gptkbp:opened |
many non-solvable groups
|
| gptkbp:relatedTo |
gptkb:inverse_Galois_problem
gptkb:Hilbert's_irreducibility_theorem gptkb:Noether's_problem |
| gptkbp:solved_for |
solvable groups
some non-solvable groups |
| gptkbp:status |
open problem
|
| gptkbp:studiedBy |
gptkb:Emil_Artin
gptkb:Jean-Pierre_Serre gptkb:Richard_Brauer |
| gptkbp:bfsParent |
gptkb:inverse_problem_of_Galois_theory
|
| gptkbp:bfsLayer |
7
|