KnowraInverse Galois problemLinked fromLinked fromThe 7 pages that link to Inverse Galois problem, each with the reason it gives.All 7Related 6Compared with 1Galois groupRelated: It asks how far abstract finite-group symmetry can arise from field extensions.Évariste GaloisRelated: It reverses Galois's central construction by asking which groups arise from equations.Galois theoryRelated: It reverses the usual direction, asking which symmetries can arise from polynomials.Class field theoryCompared with: Class field theory solves the abelian case, while the general problem concerns nonabelian groups.Chebotarev density theoremRelated: Chebotarev describes prime behavior once such a Galois realization is known, though it does not solve realization itself.Kronecker–Weber theoremRelated: The theorem completely describes which finite groups occur here in the abelian case.Belyi's theoremRelated: Belyi's theorem helps connect arithmetic actions on curves with finite permutation and Galois groups.