Class groups of dihedral extensions

Class Groups of Dihedral Extensions

Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k). 1. A Short History of Reflection Theorems Results comparing the p-rank of class groups of different number fields (often based on the interplay between Kummer theor...

Dihedral and cyclic extensions with large class numbers

This paper is a continuation of [2]. We construct unconditionally several families of number fields with large class numbers. They are number fields whose Galois closures have as the Galois groups, dihedral groups Dn, n = 3, 4, 5, and cyclic groups Cn, n = 4, 5, 6. We first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modi...

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Dihedral Groups

Limits of Dihedral Groups

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.