Finite 2-groups in which distinct nonlinear irreducible characters have distinct kernels

Abstract

In this paper, we study nite 2-groups in which distinct nonlinear irreducible characters have distinct kernels. We prove several results concerning these groups and completely classify 2-groups with at most ve nonlinear irreducible characters satisfying this property.

Keywords: Irreducible character kernels, CM-groups, CM₁-groups