2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120965In this note, we give a short proof of the existence of certain abelian extension over a given global field $K$. This result implies that for every positive integer $m$, there exists an abelian extension $L/K$ of exponent $m$ such that the $m$-torsion subgroup of $\Br(K)$ equals $\Br(L/K)$.5 pagesNumber Theory11K60, 11R29, 11R34, 11R37, 11R56, 11R58, 11S15, 11S37, 11S25text