2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142537Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l, the infinite place and only one other prime.7 pages, LaTeX; tiny changesNumber Theory11F80; 11R32text