2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208227In 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 $δ_K <2^{47/8}=58.68...$, and is totally complex.Number TheoryAlgebraic Geometry11-xx; 11Gxxtext