Finite solvable groups with two imprimitive monolithic characters

Abstract

Let G be a finite group and let χ be an irreducible character of G. If G/kerχ has a unique minimal normal subgroup, then χ is called monolithic. The character χ is said to be imprimitive if χ is induced from a character of a proper subgroup of G. In this paper, we classify the finite solvable groups having exactly two imprimitive monolithic characters whose kernels intersect trivially.