Prime graphs on the set of vanishing class sizes - Robati, Sajjad Mahmood; Hafezieh, Roghayeh (Springer-Verlag Italia Srl, 2025)
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 prove that the prime graph on the set of vanishing class sizes of a given group has at most two connected components. Moreover, we examine the class of finite solvable groups whose prime graphs associated to the set of vanishing class sizes are disconnected.
Keywords: Finite groups; Vanishing class; Irreducible characters; Prime graph