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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… Expand

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