In this paper a first step in classifying the fuzzy normal subgroups of a finite group is made. Explicit formulas for the number of distinct fuzzy normal subgroups are obtained in the particular cases of symmetric groups and dihedral groups.

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 quasisimp...