Results 31 to 40 of about 70 (70)
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Galois Groups and Fundamental Groups
2009Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful ...
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The Annals of Mathematics, 1996
This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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This paper is concerned with the connections between the Witt ring of a field and the structure of certain Galois extensions of that field. In particular, it is shown that the Witt ring determines, and is determined by, the Galois group of a certain 2-extension of the field (with an unavoidable uncertainty over the characteristic of the Witt ring in ...
Mináč, Ján, Spira, Michel
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1996
This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis.
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This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis.
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Symplectic groups as Galois groups
Journal of Group Theory, 1998This paper proves the following result: Let \(q\) be the square of an odd prime power and let \(m \geq q\). Then \(PSp(2m,q)\) is the Galois group of a regular Galois extension of \(\mathbb{Q}(x)\). The proof is an outgrowth of the idea of rigidity, but the Nielsen classes in this instance are not rigid.
Thompson, J. G., Völklein, H.
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The Primitivity of the Galois Group of a Trinomial
Journal of the London Mathematical Society, 1996The primitivity of transitive permutation groups is examined in terms of conditions on a system of generators. The authors give a criterion of primitivity for the Galois group of an irreducible trinomial with integer coefficients of the form \(X^n+ ac^n X^s+ bc^n\) using the study of the inertia groups of primes in the splitting field of such ...
Movahhedi, A., Salinier, A.
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1990
We now set up an analogy with symmetries of polygons in the plane even though some of the algebraic analogues have not yet been defined.
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We now set up an analogy with symmetries of polygons in the plane even though some of the algebraic analogues have not yet been defined.
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On the Geometrization of the Absolute Galois Group
Journal of Mathematical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Polynomials with frobenius galois groups
Communications in Algebra, 2000An effective characterization of polynomials of degree n whose Galois groups are Frobenius groups with kernel of order n is given. Some examples of such polynomials are listed.
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ABELIAN SUBGROUPS OF GALOIS GROUPS
Mathematics of the USSR-Izvestiya, 1992See the review in Zbl 0736.12004.
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