On vanishing class sizes in finite groups

Abstract

© 2017 Elsevier Inc. Let G be a finite group. An element g of G is called a vanishing element if there exists an irreducible character χ of G such that χ(g)=0; in this case, we say that the conjugacy class of g is a vanishing conjugacy class. In this paper, we discuss some arithmetical properties concerning the sizes of the vanishing conjugacy classes in a finite group