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- Inverse_Galois_problem abstract "In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th century, is unsolved.There are some permutation groups for which generic polynomials are known, which define all algebraic extensions of Q having a particular group as Galois group. These groups include all of degree no greater than 5. There also are groups known not to have generic polynomials, such as the cyclic group of order 8.More generally, let G be a given finite group, and let K be a field. Then the question is this: is there a Galois extension field L/K such that the Galois group of the extension is isomorphic to G? One says that G is realizable over K if such a field L exists.".
- Inverse_Galois_problem wikiPageExternalLink 0136.
- Inverse_Galois_problem wikiPageID "739166".
- Inverse_Galois_problem wikiPageRevisionID "596615433".
- Inverse_Galois_problem hasPhotoCollection Inverse_Galois_problem.
- Inverse_Galois_problem subject Category:Galois_theory.
- Inverse_Galois_problem subject Category:Unsolved_problems_in_mathematics.
- Inverse_Galois_problem type Abstraction100002137.
- Inverse_Galois_problem type Attribute100024264.
- Inverse_Galois_problem type Condition113920835.
- Inverse_Galois_problem type Difficulty114408086.
- Inverse_Galois_problem type Problem114410605.
- Inverse_Galois_problem type State100024720.
- Inverse_Galois_problem type UnsolvedProblemsInMathematics.
- Inverse_Galois_problem comment "In Galois theory, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th century, is unsolved.There are some permutation groups for which generic polynomials are known, which define all algebraic extensions of Q having a particular group as Galois group. These groups include all of degree no greater than 5.".
- Inverse_Galois_problem label "Inverse Galois problem".
- Inverse_Galois_problem label "Problema de Galois inverso".
- Inverse_Galois_problem label "Problema di Galois inverso".
- Inverse_Galois_problem label "Théorie de Galois inverse".
- Inverse_Galois_problem label "معضلة غالوا العكسية".
- Inverse_Galois_problem sameAs Problema_de_Galois_inverso.
- Inverse_Galois_problem sameAs Théorie_de_Galois_inverse.
- Inverse_Galois_problem sameAs Problema_di_Galois_inverso.
- Inverse_Galois_problem sameAs Problema_inverso_de_Galois.
- Inverse_Galois_problem sameAs m.03777r.
- Inverse_Galois_problem sameAs Q2358071.
- Inverse_Galois_problem sameAs Q2358071.
- Inverse_Galois_problem sameAs Inverse_Galois_problem.
- Inverse_Galois_problem wasDerivedFrom Inverse_Galois_problem?oldid=596615433.
- Inverse_Galois_problem isPrimaryTopicOf Inverse_Galois_problem.