Groups whose vanishing class sizes are p-powers

Abstract

Given a finite group G, an element is called a vanishing element of G if it is a zero of an irreducible character of G; otherwise, it is called a non-vanishing element. Moreover, the conjugacy class of an element is termed as a vanishing class if that element is a vanishing element. In this paper, we describe the finite groups whose vanishing class sizes are all powers of a prime p.