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| 关于Thompson猜想与AAM猜想 |
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张良才,施武杰,王玲丽
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1. 重庆大学数理学院,重庆,400044
2. 苏州大学数学科学学院,江苏,苏州,215006
3. 中北大学理学院数学系,山西,太原,030051
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| 摘要: |
| 本文研究了有限(几乎)单群的非交换图刻画问题.利用有限几乎单群的阶分量理论,证明了对于具有非连通素图的有限单群,AAM猜想成立,同时也证明了某砦几乎单群也能被其非交换图刻画.上述结果推广了文献f131的结果.Abstract：In this article,we discuss the characterization of some finite(almost)simple groups by their non-commuting graphs.By using the theory of order components of finite almost simple groups,we prove that AAM's conjecture is true for all finite simple groups with non-connected prime graphs.Moreover,we prove that some almost simple groups can be also characterized by their non-commuting graphs.All the above results generalize those results in[13]. |
| 关键词: 有限群 非交换图 阶分量 Thompson猜想 AAM猜想 |
| DOI： |
| 分类号:O152.1 |
| 基金项目:Supported by the National Natural Science Foundation of China，the SRFDP of China，a Subproject of the NNSF of China，Chongqing University |
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| ON THOMPSON'S CONJECTURE AND AAM'S CONJECTURE |
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ZHANG Liang-cai,SHI Wu-jie,WANG Ling-li
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ZHANG Liang-cai1,SHI Wu-jie2,WANG Ling-li3 (1. College of Math. and Physics,Chongqing University,Chongqing 400044,China) (2. School of Math. Sciences,Suzhou University,Suzhou 215006,China) (3. Dept. of Math. of College of Science,North University of China,Taiyuan 030051,China)
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| Abstract: |
| In this article,we discuss the characterization of some finite(almost)simple groups by their non-commuting graphs.By using the theory of order components of finite almost simple groups,we prove that AAM's conjecture is true for all finite simple groups with non-connected prime graphs.Moreover,we prove that some almost simple groups can be also characterized by their non-commuting graphs.All the above results generalize those results in[13]. |
| Key words: finite group non-commuting graph order component Thompson's conjecture AAM's conjecture |
