Extendible characters and monomial groups of odd order

Let G be a finite p-solvable group, where p is an odd prime. We establish a connection between extendible irreducible characters of subgroups of G that lie under monomial characters of G and nilpotent subgroups of G. We also provide a way to get “good” extendible irreducible characters inside subgroups of G. As an application, we show that every normal subgroup N of a finite monomial odd p,q-group G, that has nilpotent length less than or equal to 3, is monomial.