On open normal subgroups of parahorics

Let F be a local complete field with discrete valuation, and let G be a quasisplit group over F which splits over some unramified extension of F . Let P be a parahoric subgroup of the group G(F ) of F -points of G; the open normal pronilpotent subgroups of P can be classified using the standard normal filtration subgroups of Prasad and Raghanathan. More precisely, we show that if G is quasisimple and satisfies some additional conditions, H is, modulo a subgroup of some maximal torus of G, either one of these filtration subgroups or the product of one of them by a standard normal filtration subgroup of P ∩ M , where M is a proper Levi subgroup of G.