Non-solvable groups each of whose vanishing class sizes has at most two prime divisors

Abstract

Let G be a finite group. A classical theorem of Burnside shows that a group with order divisible by at most two primes is solvable. The aim of this article is studying finite groups each of whose vanishing class sizes has at most two prime divisors, where a conjugacy class of x in G is a vanishing class if there exists some irreducible character χ of G such that $\chi (x)=0.$

Keywords:

• Non-solvable groups
• prime graphs
• vanishing class sizes

Mathematics Subject Classification (2010):

• 20C15
• 20E45

Acknowledgment

The author is grateful to the referee for their valuable comments.