Let $G$ be a finite group and let $\chi$ be a complex character of $G$. It's well known that the product of $\chi\overline{\chi}$ is also a character of the group $G$, where $\overline{\chi}$ is the complex conjugate character of $\chi$. In this talk, we give some results about the relationship between the structure of the group $G$ and the kernels of irreducible constituents of the character $\chi\overline{\chi}$ where $\chi $ is a nonlinear irreducible character of $G$.