A New Characterization of PSL(2, q) by Group Order and the Set of Vanishing Element Orders

• 来源期刊: 代数集刊（英文版）
• 关键词: finite simple group vanishing element order prime graph projective special linear group
• 年，卷（期）: 2019,（3）
• 页码范围: 459-466
• 页数: 8页
• 语种: 英文
• DOI: 10.1142/S1005386719000336

摘要

An element g in a finite group G is called a vanishing element if there exists some irreducible complex character x of G such that x(g) =0.Denote by Vo(G) the set of orders of vanishing elements of G,and we prove that G ≌ PSL(2,q) if and only if |G| =|PSL(2,q)| and Vo(G) =Vo(PSL(2,q)),where q ≥ 4 is a prime power.