MONOMIAL A D MONOLITHIC CHARACTERS OF FINITE SOLVABLE GROUPS

Abstract

Let G be a finite solvable group and let p be a prime divisor of vertical bar G vertical bar. We prove that if every monomial monolithic character degree of G is divisible by p, then G has a normal p-complement and, if p is relatively prime to every monomial monolithic character degree of G, then G has a normal Sylow p-subgroup. We also classify all finite solvable groups having a unique imprimitive monolithic character.