p-Groups in which kernels of the non-linear irreducible characters are of equal order

Abstract

For an irreducible character $\chi$ of a finite group $G$, its kernel is defined as $\text{ker }\chi =\{g\in G:\chi (g)=\chi (1)\}$. In this paper we characterize the finite groups of prime power order(for odd prime) in which kernels of all of the non-linear irreducible characters are of the same order.