NON-VANISHING ELEMENTS AND ZEROS OF CHARACTERS OF FINITE GROUPS: A REVIEW

Let G be a finite group. A well-known result of W. Burnside tells us that, for any nonlinear irreducible character  of G, there exists an element g 2 G such that Â(g) = 0. In this paper, first we investigate elements g 2 G fulfilling that all the irreducible characters take non-zero values at g . Then, we deal with the number of conjugacy classes of G where  vanishes, for a fixed irreducible character Â.