A new characterization of A_p(2) and A_p-1(2) where 2^p- 1 is a prime

چکیده مقاله

Let G be a finite group, and Irr(G) be the set of complex irreducible characters of G. An element g ∈ G is called a vanishing element if there exists an irreducible character χ ∈ Irr(G) such that χ(g) = 0. The set of orders of vanishing elements of G is denoted by Vo(G). A recent conjecture states that if G is a finite group and M is a finite nonabelian simple group such that Vo(G) = Vo(M) and (G) = (M), then G ≅ M. In this paper, we give a positive answer to this conjecture for a family of classical simple groups, namely Ap(2) and A_p-1(2), where p ≠ 2; 3 and 2^p-1 is a prime. © 2019 Editura Academiei Romane. All rights reserved.