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Displaying 321 – 340 of 453

Principalization algorithm via class group structure

Daniel C. Mayer (2014)

Journal de Théorie des Nombres de Bordeaux

For an algebraic number field $K$ with $3$ -class group ${Cl}_{3} (K)$ of type $(3, 3)$ , the structure of the $3$ -class groups ${Cl}_{3} (N_{i})$ of the four unramified cyclic cubic extension fields $N_{i}$ , $1 \leq i \leq 4$ , of $K$ is calculated with the aid of presentations for the metabelian Galois group $G_{3}^{2} (K) = Gal (F_{3}^{2} (K) | K)$ of the second Hilbert $3$ -class field $F_{3}^{2} (K)$ of $K$ . In the case of a quadratic base field $K = ℚ (\sqrt{D})$ it is shown that the structure of the $3$ -class groups of the four $S_{3}$ -fields $N_{1}, ..., N_{4}$ frequently determines the type of principalization of the $3$ -class group of $K$ in $N_{1}, ..., N_{4}$ . This provides...

Quadratic Equations over Finite Fields and Class Numbers of Real Quadratic Fields.

Takashi Agoh, Toshiaki Shoji (1998)

Monatshefte für Mathematik

Quadratic extensions of quintic fields of signature $(3, 1)$

Schehrazad Selmane (2002)

Acta Mathematica et Informatica Universitatis Ostraviensis

Quadratic fields with infinite Hilbert 2-class field towers

Frank Gerth III (2003)

Acta Arithmetica

Quadratic function fields whose class numbers are not divisible by three

Humio Ichimura (1999)

Acta Arithmetica

Quadratic polynomials producing consecutive, distinct primes and class groups of complex quadratic fields

R. A. Mollin (1996)

Acta Arithmetica

Quadratische Formen und quadratische Reziprozitätsgesetze über algebraischen Zahlkörpern.

W. Scharlau, M. Knebusch (1971)

Mathematische Zeitschrift

Ray class fields of global function fields with many rational places

Roland Auer (2000)

Acta Arithmetica

Real Quadratic Number Fields with 2-Class Group of Type (2,2).

Elliot Benjamin, C. Snyder (1995)

Mathematica Scandinavica

Real quadratic number fields with metacyclic Hilbert $2$ -class field tower

Said Essahel, Ahmed Dakkak, Ali Mouhib (2019)

Mathematica Bohemica

We begin by giving a criterion for a number field $K$ with 2-class group of rank 2 to have a metacyclic Hilbert 2-class field tower, and then we will determine all real quadratic number fields $ℚ (\sqrt{d})$ that have a metacyclic nonabelian Hilbert $2$ -class field tower.