Background
Type: Article

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

Journal: Mathematical Reports (15823067)Year: 2019Volume: 21Issue: Pages: 431 - 440
Language: English

Abstract

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 Ap-1(2), where p ≠ 2; 3 and 2p-1 is a prime. © 2019 Editura Academiei Romane. All rights reserved.