A non-solvable Galois extension of $\Q$ ramified at 2 only

TL;DR

This paper constructs a specific non-solvable Galois extension of the rational numbers ramified only at 2, with detailed properties including degree, discriminant, and complex structure, expanding understanding of ramification in number fields.

Contribution

It demonstrates the existence of a non-solvable Galois extension of bc ramified solely at 2, with explicit degree and discriminant, which was previously unknown.

Findings

Extension has degree 2^{19}(3*5*17*257)^2

Root discriminant is less than 58.68

Extension is totally complex

Abstract

In this paper, we show the existence of a non-solvable Galois extension of $\Q$ which is unramified outside 2. The extension $K$ we construct has degree $2251731094732800=2^{19}(3\cdot 5\cdot 17\cdot 257)^2$ and has root discriminant $\delta_K <2^{{47/8}}=58.68...$, and is totally complex.