ON THE ORDERS OF ZEROS OF STRONGLY MONOLITHIC CHARACTERS

Let G be a finite group and p be a prime number. An element g of G is called an $\mathrm {SM}<^>*$ -vanishing element of G if there exists a strongly monolithic character $\chi $ of G satisfying $Z(\chi )=\ker \chi $ and $\chi (g)=0$ . In this paper, we present some results on the relationship between the orders of $\mathrm {SM}<^>*$ -vanishing elements of G and the structure of G.