• Corpus ID: 119160385

A remark On Abelianized Absolute Galois Group of Imaginary Quadratic Fields

@article{Smit2017ARO,
  title={A remark On Abelianized Absolute Galois Group of Imaginary Quadratic Fields},
  author={Bart de Smit and Pavel Solomatin},
  journal={arXiv: Number Theory},
  year={2017}
}
The main purpose of this paper is to extend results on isomorphism types of the abelianized absolute Galois group $\mathcal G_K^{ab}$, where $K$ denotes imaginary quadratic field. In particular, we will show that if the class number $h_K$ of an imaginary quadratic field $K$ different from $\mathbb Q(i)$, $\mathbb Q(\sqrt{-2})$ is a fixed prime number $p$ then there are only two isomorphism types of $\mathcal G_K^{ab}$ which could occur. For instance, this result implies that imaginary quadratic… 

References

SHOWING 1-4 OF 4 REFERENCES
On Abelianized Absolute Galois Group of Global Function Fields
The main purpose of this paper is to describe the abelian part $\mathcal G^{ab}_{K}$ of the absolute Galois group of a global function field $K$ as pro-finite group. We will show that the
Imaginary quadratic fields with isomorphic abelian Galois groups
In 1976, Onabe discovered that, in contrast to the Neukirch-Uchida results that were proved around the same time, a number field $K$ is not completely characterized by its absolute abelian Galois
Pontryagin Duality and the Structure of Locally Compact Abelian Groups
1. Introduction to topological groups 2. Subgroups and quotient groups of Rn 3. Uniform spaces and dual groups 4. Introduction to the Pontryagin-van Kampen duality theorem 5. Duality for compact and