A new characterization of some finite simple groups

Let G be a finite group. A vanishing element of G is g ∈ G such that χ ( g ) = 0 for some χ ∈ Irr( G ) of the set of irreducible complex characters of G . Denote by Vo( G ) the set of the orders of vanishing elements of G . A finite group G is called a VCP- group if every element in Vo( G ) is of prime power order. The main purpose of this paper is to investigate a new characterization related to Vo( G ) for all finite nonabelian simple VCP-groups. We prove that if G is a finite group and M is a finite nonabelian simple VCP-group such that Vo( G ) = Vo( M ) and | G | = | M |, then G ≅ M .