On Covering Number of Groups with Trivial Fitting Subgroup

作     者：Yang LIU Yang LIU

作者机构：School of Mathematical ScienceTianjin Normal UniversityTianjin 300387P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第7期

页      面：1277-1284页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the Science&Technology Development Fund of Tianjin Education Commission for Higher Education(Grant No.2020KJ010) 

主　　题：Character degree covering number nonsolvable group 

摘      要：Let G be a finite group and S be a subset of Irr(G).If for every prime divisor p of|G|there is a characterχin S such that p dividesχ(1),S is called a covering set of *** covering number of G,denoted by cn(G),is defined as the minimal number of Card(S),where S is a covering set of G and Card(S)is the cardinality of set *** this paper,we prove that if G is a finite group with F(G)=1,then the covering number cn(G)≤***,if PSL2(q)or J1 is not involved in G,then cn(G)≤2.