Some Simple Groups Which are Determined by Their Orders and Degree-Patterns  

作　　者：Qinghong Guo Weijun Liu Genghua Fan 

机构地区：[1]School of Mathematics and Statistics,HNP-LAMA,Central South University Changsha 410083,China [2]College of General Education,Guangdong University of Science and Technology Dongguan,Guangdong 523083,China [3]不详

出　　处：《Algebra Colloquium》2024年第2期341-346,共6页代数集刊（英文版）

基　　金：supported by NSFC(12071484);Hunan Provincial Natural Science Foundation(2020JJ4675);Foundation of Guangdong University of Science and Technology.

摘　　要：Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.

关 键 词：irreducible complex character character-prime graph finite nonabelian simple group 

分 类 号：O15[理学—数学]