| 单群A8与L3(4)的新刻画 |
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| 引用本文： | 刘鑫,杨梅,晏燕雄.单群A8与L3(4)的新刻画[J].西南师范大学学报(自然科学版),2020,45(4):5-8. |
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| 作者姓名： | 刘鑫 杨梅 晏燕雄 |
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| 作者单位： | 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 |
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| 基金项目： | 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）. |
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| 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A_8和L_3(4).
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| 关 键 词： | 单群 群的阶 特征标维数 |
| 收稿时间： | 2019/12/15 0:00:00 |
A New Characterization of Simple Group A8 and L3(4) |
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| LIU Xin,YANG Mei,YAN Yan-xiong.A New Characterization of Simple Group A8 and L3(4)[J].Journal of Southwest China Normal University(Natural Science),2020,45(4):5-8. |
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| Authors: | LIU Xin YANG Mei YAN Yan-xiong |
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| Institution: | 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;2. School of General Education and International Studies, Chongqing College of Electronic Engineering, Chongqing 401331, China |
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| Abstract: | 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. |
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| Keywords: | simple group order of finite group character degree |
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