The 6-step Solvable Mono-anabelian Reconstruction of Abelian Number Fields

TL;DR

This paper introduces a novel 6-step solvable group-theoretic method to reconstruct abelian number fields independently of previous bi-anabelian approaches, advancing the understanding of number field reconstruction.

Contribution

It presents a new, independent method for reconstructing abelian number fields from their Galois groups using a 6-step solvable quotient, distinct from prior bi-anabelian techniques.

Findings

Reconstruction of abelian number fields from Galois groups is possible via a 6-step solvable quotient.

The method is independent of bi-anabelian results by Saidi and Tamagawa.

Provides a new framework for number field reconstruction using solvable group quotients.

Abstract

In this paper, we develop a new method to reconstruct an abelian number field $K$ from the maximal $6$-step solvable quotient of $G_K$ group- theoretically. The new aspect of this paper is that the results in this paper are independent from the bi-anabelian results proved proven by Saidi and Tamagawa in [ST22].