Results 1 to 10 of about 23,993 (138)
On the inverse problem of Galois theory [PDF]
Transactions of the American Mathematical Society, 1975 Let k k be a field, F F a finite subfield and G G a connected solvable algebraic matric group defined over F F . Conditions on G G and k k are given which ensure the existence of a Galois extension of k k with group isomorphic to
J. Kovacic
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On the inverse problem of Galois theory [PDF]
Publicacions Matemàtiques, 1992 The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
Núria Vila
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On the Inverse Problem of Galois Theory of Differential Fields [PDF]
Proceedings of the American Mathematical Society, 1964 1. All fields considered here are of characteristic 0. Let F be a field, let C be an algebraically closed subfield of F. Let G be a connected algebraic group defined over C. F(G) denotes the field of all rational functions on G defined over F. If gCG then F(g) denotes the field generated by g over F. We shall say that a derivation of F(G) commutes with
A. Bialynicki-Birula
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Differential Galois theory III: Some inverse problems [PDF]
Illinois Journal of Mathematics, 1997 [For Part I see ibid. 42, No. 4, 678-699 (1998; Zbl 0916.03028). Part II is reviewed above.] In Part I, the author developed a theory of differential Galois extensions, generalizing Kolchin's theory of strongly normal extensions. It was shown that arbitrary finite-dimensional differential algebraic groups can arise as differential Galois groups for ...
David Marker, Anand Pillay
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Semi-topological Galois theory and the inverse Galois problem [PDF]
, 2010 23 ...
Hsuan-Yi Liao, Jyh-Haur Teh
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Galois Theory for Inverse Semigroup Orthogonal Actions [PDF]
, 2020 A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of inverse semigroup theory that establishes a one-to-one correspondence between inverse semigroups and inductive groupoids.
Wesley G. Lautenschlaeger +1 more
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The $q$-analogue of the wild fundamental group and the inverse problem of the Galois theory of $q$-difference equations [PDF]
Annales scientifiques de l'École normale supérieure, 2015 In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem. In this paper, we completely describe the wild fundamental group and apply this result to the inverse problem in $q$-difference Galois theory.
Jean-Pierre Ramis, Jacques Sauloy
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On the Inverse Problem in Differential Galois Theory
, 2002 Differential Galois theory generalizes the usual Galois theory for polynomials to differential equations. There is the notion of a splitting field (Picard-Vessiot extension) of a differential equation, and the differential Galois group is the group of automorphisms of this extension which fix the base field and commute with the derivation. Differential
Julia Hartmann
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On the finite inverse problem in iterative differential Galois theory [PDF]
, 2010 In positive characteristic, nearly all Picard-Vessiot extensions are inseparable over some intermediate iterative differential extensions. In the Galois correspondence, these intermediate fields correspond to nonreduced subgroup schemes of the Galois group scheme. Moreover, the Galois group scheme itself may be nonreduced, or even infinitesimal.
Andreas Maurischat
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Demushkin groups and inverse Galois theory for pro-p-groups of finite rank and maximal p-extensions [PDF]
, 2011 LaTex, 28 pages; an inaccuracy in the proof of Lemma 3.2 is fixed; improvements in the presentation at several other ...
Ivan D. Chipchakov
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