Normal subgroups of odd-order monomial $p^a{q}^b$ groups

Abstract

A finite group $G$ is called monomial if every irreducible character of $G$ is induced from a linear character of some subgroup of $G$. One of the main questions regarding monomial groups is whether or not a normal subgroup $N$ of a monomial group $G$ is itself monomial. In the case that $G$ is a group of even order, it has been proved (Dade, van der Waall) that $N$ need not be monomial. Here we show that, if $G$ is a monomial group of order $p^a{q}^b$, where $p$ and $q$ are distinct odd primes, then any normal subgroup $N$ of $G$ is also monomial.

PhD Thesis, Univ. of Illinois 2001, advisor E. Dade

Cited by in corpus (1)

• Linear limits of irreducible characters