Results 11 to 20 of about 70 (70)
On Galois Conditions and Galois Groups of Simple Rings [PDF]
Transactions of the American Mathematical Society, 1965 Throughout the present paper, R will be a simple ring, where we shall understand by a simple ring a total matrix ring over a division rings. If S' is any subring containing the identity element 1 of R, we denote by VR(S') the centralizer of S' in R, VR(S') = VR(VR(S')) and by 0 (S', R) we denote the group of all automorphisms of R which are the ...
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Symplectic Groups as Galois Groups
Journal of Algebra, 2000 Let \(\mathbb{F}\) be a field containing the field of order \(q\), let \(x\) and \(t\) be indeterminates, let \(m\) be an integer greater than 1, and let \[ \widehat{f}(Y)= Y^{q^{2m}}+ t^q Y^{q^{m+1}}+ xY^{q^m}+ tY^{q^{m-1}}+Y. \] In [\textit{S. S. Abhyankar}, Proc. Am. Math. Soc. 124, 2977--2991 (1996; Zbl 0866.12005)], it was shown that, for \(m>2\),
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Construction and Characterization of Galois Algebras with Given Galois Group [PDF]
Nagoya Mathematical Journal, 1950 Recently H. Hasse has given an interesting theory of Galois algebras, which generalizes the well known theory of Kummer fields; an algebra over a field Ω is called a Galois algebra with Galois group G when possesses G as a group of automorphisms and is (G, Ω)-operator-isomorphic to the group ring G(Ω) of G over Ω. On assuming that the characteristic
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On the Distribution of Galois Groups
Journal of Number Theory, 2002 \(K\) sei ein algebraischer Zahlkörper und \(G\) eine transitive Untergruppe der symmetrischen Gruppe \(S_n\). Es wird eine Vermutung formuliert betreffend des Wachstums der Funktion \(Z(K,G,x)\), welche die Anzahl derjenigen Körpererweiterungen \(L/K\) vom Grade \(n\) angibt, für die die Galoissche Hülle bez.
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Projective isomonodromy and Galois groups [PDF]
Proceedings of the American Mathematical Society, 2012 In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy-evolving deformation of linear differential equations, based on the example of the Darboux-Halphen equation. We give an algebraic condition for a parameterized linear differential equation to be projectively isomonodromic, in terms of the derived ...
Mitschi, Claude, Singer, Michael F.
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On the definitions of difference Galois groups [PDF]
, 2008 We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of Picard-Vessiot extensions over fields with not necessarily algebraically closed subfields of constants.
Chatzidakis, Zoé +2 more
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On the Galois Structure of Selmer Groups [PDF]
International Mathematics Research Notices, 2015 Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the explicit Galois structure of the p-primary Selmer group of A over F.
Burns, David +2 more
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A note on the quaternion group as Galois group [PDF]
Proceedings of the American Mathematical Society, 1990 The occurrence of the quaternion group as a Galois group over certain fields is investigated. A theorem of Witt on quaternionic Galois extensions plays a key role.
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The Valentiner group as Galois group [PDF]
Proceedings of the American Mathematical Society, 2004 We obtain the complete set of solutions to the Galois embedding problem given by the Valentiner group as a triple cover of the alternating group A 6 A_6 .
Crespo Vicente, Teresa, Hajto, Zbigniew
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Schur Indices and the Galois Group [PDF]
Proceedings of the American Mathematical Society, 1981 In this note we show that the order of the Schur index of an irreducible representation divides the order of a certain subgroup of the Galois group of a cyclotomic extension of the ground field.
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