Description of Galois unipotent extensions

TL;DR

This paper characterizes all Galois extensions of an arbitrary field with Galois groups isomorphic to the group of upper triangular unipotent 4x4 matrices over the field of two elements, providing a complete description.

Contribution

It provides a comprehensive description of Galois extensions with a specific unipotent matrix group as their Galois group, extending understanding of such extensions.

Findings

Complete classification of Galois extensions with the specified Galois group.

Explicit description of the structure of these extensions.

Advances the understanding of unipotent Galois groups over arbitrary fields.

Abstract

Given an arbitrary field $F$, we describe all Galois extensions $L/F$ whose Galois groups are isomorphic to the group of upper triangular unipotent 4-by-4 matrices with entries in the field of two elements.