  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.

Group Theory