单群A8与L3(4)的新刻画  

A New Characterization of Simple Group A8 and L3(4)

作　　者：刘鑫 杨梅[2] 晏燕雄[1] LIU Xin;YANG Mei;YAN Yan-xiong(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;School of General Education and International Studies, Chongqing College of Electronic Engineering, Chongqing 401331, China)

机构地区：[1]西南大学数学与统计学院,重庆400715 [2]重庆电子工程职业学院通识教育与国际学院,重庆401331

出　　处：《西南师范大学学报（自然科学版）》2020年第4期5-8,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11171364,11271301);中央高校专项基金项目(XDJK2019C116,XDJK2019B030);西南大学教改项目(2018JY061).

摘　　要：众所周知,有限群的特征标维数图对群的结构有重要的影响.Huppert猜想提出:有限非交换单群能够被它的所有不可约特征标维数集所刻画.利用群的特征标维数刻画群的结构是研究有限群的一个重要方法.继续这一相关问题的研究,研究了群的特征标维数幂图与群结构的关系,并利用群的阶与群的不可约特征标维数幂图成功地刻画了单群A8和L3(4).It is well known that the character dimension graph of a finite group has an important influence on the structure of a group.The Huppert's conjecture proposed that all finite non-abelian simple groups can be characterized by the set of their irreducible character degrees.It is an important method to characterize the structure of a finite group by using its characteristic dimension.In this paper,we continue to investigate this topic,and study the relationship between the dimension power graph and the structure of a finite group.In particular,we successfully characterize the simple group A8 and L3(4)by their order and dimension power graph.

关 键 词：单群 群的阶 特征标维数 

分 类 号：O152.1[理学—数学]