2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99989Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution s of G. We prove a polar decomposition G=KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of the groups of k-points of maximal (k,s)-split tori, one for each H-conjugacy class. This decomposition is analogous to the well-known polar decomposition G=KAH for a real symmetric space G/H.16 pagesGroup TheoryNumber Theory20G25text