Extendible characters and monomial groups of odd order

Details Extendible characters and monomial groups of odd order Extendible characters and monomial groups of odd order

2004-12-19

arxiv.org/abs/math/0412383v1

Mathematics

Group Theory

Scientific paper

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.

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