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Displaying 161 – 180 of 278

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...

Products of finite nilpotent groups.

Hermann Heineken (1990)

Mathematische Annalen

Products of Fitting Classes.

John Cossey (1975)

Mathematische Zeitschrift

Proiettività dei $p$ -gruppi di classe massimale

Andrea Caranti (1979)

Rendiconti del Seminario Matematico della Università di Padova

Projectivities in Finite Abelian p-Groups.

Karl H. Wehrhahn (1971)

Mathematische Zeitschrift

Properties of subgroups not containing their centralizers

Lemnouar Noui (2009)

Annales mathématiques Blaise Pascal

In this paper, we give a generalization of Baer Theorem on the injective property of divisible abelian groups. As consequences of the obtained result we find a sufficient condition for a group $G$ to express as semi-direct product of a divisible subgroup $D$ and some subgroup $H$ . We also apply the main Theorem to the $p$ -groups with center of index $p^{2}$ , for some prime $p$ . For these groups we compute $N_{c} (G)$ the number of conjugacy classes and $N_{a}$ the number of abelian maximal subgroups and $N_{n a}$ the number of nonabelian...