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- Generic_polynomial abstract "In Galois theory, a branch of modern algebra, a generic polynomial for a finite group G and field F is a monic polynomial P with coefficients in the field L = F(t1, ..., tn) of F with n indeterminates adjoined, such that the splitting field M of P has Galois group G over L, and such that every extension K/F with Galois group G can be obtained as the splitting field of a polynomial which is the specialization of P resulting from setting the n indeterminates to n elements of F. This is sometimes called F-generic relative to the field F, with a Q-generic polynomial, generic relative to the rational numbers, being called simply generic.The existence, and especially the construction, of a generic polynomial for a given Galois group provides a complete solution to the inverse Galois problem for that group. However, not all Galois groups have generic polynomials, a counterexample being the cyclic group of order eight.".
- Generic_polynomial wikiPageID "1400173".
- Generic_polynomial wikiPageLength "3836".
- Generic_polynomial wikiPageOutDegree "19".
- Generic_polynomial wikiPageRevisionID "657189696".
- Generic_polynomial wikiPageWikiLink Category:Field_theory.
- Generic_polynomial wikiPageWikiLink Category:Galois_theory.
- Generic_polynomial wikiPageWikiLink Cyclic_group.
- Generic_polynomial wikiPageWikiLink Dihedral_group.
- Generic_polynomial wikiPageWikiLink Direct_product_of_groups.
- Generic_polynomial wikiPageWikiLink Field_(mathematics).
- Generic_polynomial wikiPageWikiLink Finite_group.
- Generic_polynomial wikiPageWikiLink Galois_group.
- Generic_polynomial wikiPageWikiLink Galois_theory.
- Generic_polynomial wikiPageWikiLink Gene_Ward_Smith.
- Generic_polynomial wikiPageWikiLink Heisenberg_group.
- Generic_polynomial wikiPageWikiLink Hendrik_Lenstra.
- Generic_polynomial wikiPageWikiLink Indeterminate.
- Generic_polynomial wikiPageWikiLink Inverse_Galois_problem.
- Generic_polynomial wikiPageWikiLink Monic_polynomial.
- Generic_polynomial wikiPageWikiLink Quaternion_group.
- Generic_polynomial wikiPageWikiLink Splitting_field.
- Generic_polynomial wikiPageWikiLink Symmetric_group.
- Generic_polynomial wikiPageWikiLink Wreath_product.
- Generic_polynomial wikiPageWikiLinkText "generic cyclic polynomial".
- Generic_polynomial wikiPageWikiLinkText "generic polynomial".
- Generic_polynomial subject Category:Field_theory.
- Generic_polynomial subject Category:Galois_theory.
- Generic_polynomial hypernym P.
- Generic_polynomial type Album.
- Generic_polynomial comment "In Galois theory, a branch of modern algebra, a generic polynomial for a finite group G and field F is a monic polynomial P with coefficients in the field L = F(t1, ..., tn) of F with n indeterminates adjoined, such that the splitting field M of P has Galois group G over L, and such that every extension K/F with Galois group G can be obtained as the splitting field of a polynomial which is the specialization of P resulting from setting the n indeterminates to n elements of F.".
- Generic_polynomial label "Generic polynomial".
- Generic_polynomial sameAs Q5532677.
- Generic_polynomial sameAs m.04zkty.
- Generic_polynomial sameAs Q5532677.
- Generic_polynomial wasDerivedFrom Generic_polynomial?oldid=657189696.
- Generic_polynomial isPrimaryTopicOf Generic_polynomial.