Relative Pólya group and Pólya dihedral extensions of Q

  title={Relative P{\'o}lya group and P{\'o}lya dihedral extensions of Q},
  author={Ali Rajaei and Abbas Maarefparvar},
  journal={Journal of Number Theory},

P\'olya-Ostrowski Group and Unit Index in Real Biquadratic Fields

Pólya group of a Galois number field K is the subgroup of the ideal class group of K generated by all strongly ambiguous ideal classes. In this paper, using Galois cohomology and some results in [14,

Totally real bi-quadratic fields with large Pólya groups

For an algebraic number field K with ring of integers OK , an important subgroup of the ideal class group ClK is the Pólya group, denoted by Po(K), which measures the failure of the OK -module

Ostrowski quotients for finite extensions of number fields

. For L/K a finite Galois extension of number fields, the relative P´olya group Po( L/K ) coincides with the group of strongly ambiguous ideal classes in L/K . In this paper, using a well known exact

Pre-Pólya group in even dihedral extensions of ℚ

Investigating on Pólya groups [P. J. Cahen and J. L. Chabert Integer-Valued Polynomials, Mathematical Surveys and Monographs, Vol. 48 (American Mathematical Society, Providence, 1997)] in non-Galois

The analogue of the BRZ exact sequence for Tate-Shafarevich Groups

We find an exact sequence in term of Tate-Shafarevich groups (assuming being finite) X(E/K) and X(E/L) of elliptic curve E over a finite Galois extension L/K of number fields. This is the analogue of

Existence of relative integral basis over quadratic fields and Pólya property

For $$L/K$$ L / K a finite extension of algebraic number fields, L may or may not have a relative integral basis over K. We show the existence of relative integral basis of a biquadratic field



Biquadratic Pólya fields with only one quadratic Pólya subfield

Pólya S3-extensions of ℚ

Abstract A number field K with a ring of integers 𝒪K is called a Pólya field, if the 𝒪K-module of integer-valued polynomials on 𝒪K has a regular basis, or equivalently all its Bhargava factorial

Cubic, quartic and sextic Pólya fields

Some non-Pólya biquadratic fields with low ramification

Polya fields are fields with principal Bhargava factorial ideals, and as a generalization of class number one number fields, their classification might be of interest to number theorists. It is known

Class Number and Ramification in Number Fields

In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk , the class number of K. The

On generic polynomials

A note on class numbers of algebraic number fields

About the embedding of a number field in a Pólya field

Class Field Theory

A Brief Review.- Dirichlet#x2019 s Theorem on Primes in Arithmetic Progressions.- Ray Class Groups.- The Id#x00E8 lic Theory.- Artin Reciprocity.- The Existence Theorem, Consequences and

Integer valued polynomials over a number field

A number field is called a Pólya field if the module of integer valued polynomials over that field is generated by (fi)i=0∞ over the ring of integers, with deg(fi)=i, i=0, 1, 2,... In this paper