On finite linear groups stable under Galois operation.

Khrebtova, Ekaterina; Malinin, Dmitry

Displaying similar documents to “On finite linear groups stable under Galois operation.”

On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.

Chipchakov, Ivan D. (2005)

Acta Universitatis Apulensis. Mathematics - Informatics

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Corrigendum: "Galois groups of trinomials" (Acta Arith. 54 (1989), 43-49)

S. D. Cohen (1995)

Acta Arithmetica

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Criterion for a field to be abelian

J. Wójcik (1995)

Colloquium Mathematicae

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Galois-type connections and closure operations on preordered sets.

Száz, Árpád (2009)

Acta Mathematica Universitatis Comenianae. New Series

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A classification of the extensions of degree $p^{2}$ over $ℚ_{p}$ whose normal closure is a $p$ -extension

Luca Caputo (2007)

Journal de Théorie des Nombres de Bordeaux

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Let $k$ be a finite extension of $ℚ_{p}$ and $ℰ_{k}$ be the set of the extensions of degree $p^{2}$ over $k$ whose normal closure is a $p$ -extension. For a fixed discriminant, we show how many extensions there are in $ℰ_{ℚ_{p}}$ with such discriminant, and we give the discriminant and the Galois group (together with its filtration of the ramification groups) of their normal closure. We show how this method can be generalized to get a classification of the extensions in $ℰ_{k}$ .

Equivariant Weierstrass preparation and values of $L$ -functions at negative integers.

Burns, David, Greither, Cornelius (2003)

Documenta Mathematica

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Module structure of integers in metacyclic extensions

James Carter (1998)

Colloquium Mathematicae

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Constructing class fields over local fields

Sebastian Pauli (2006)

Journal de Théorie des Nombres de Bordeaux

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Let $K$ be a $𝔭$ -adic field. We give an explicit characterization of the abelian extensions of $K$ of degree $p$ by relating the coefficients of the generating polynomials of extensions $L / K$ of degree $p$ to the exponents of generators of the norm group $N_{L / K} (L^{*})$ . This is applied in an algorithm for the construction of class fields of degree $p^{m}$ , which yields an algorithm for the computation of class fields in general.