When is a 2-Power Cyclotomic Extension cyclic?

TL;DR

This paper investigates the conditions under which 2-power cyclotomic extensions are cyclic, analyzing Galois group structures, subextensions, tower decompositions, and base field properties to provide a comprehensive characterization.

Contribution

It offers a detailed characterization of the cyclicity of 2-power cyclotomic extensions based on Galois groups and base field conditions, advancing understanding in algebraic number theory.

Findings

Identifies specific conditions on the base field for cyclicity.

Describes the structure of Galois groups in these extensions.

Provides criteria for tower decompositions and subextensions.

Abstract

This paper characterizes the cyclicity property of $2$-power cyclotomic extensions through various means: the structure of the Galois groups, the nature of their subextensions, tower decompositions, and, most importantly, specific conditions on the base field.