| 张良才,施武杰,刘雪峰.L4(4)的非交换图刻画[J].数学年刊A辑,2009,30(4):517~524 |
| L4(4)的非交换图刻画 |
| A Characterization of L-4(4)by Its Noncommuting Graph |
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| DOI： |
| 中文关键词: 有限群 非交换图 AAM猜想 射影特殊线性单群 |
| 英文关键词:Finite group, Noncommuting graph, AAM’s conjecture, Projective special
linear simple group |
| 基金项目:国家自然科学基金，教育部新世纪优秀人才支持计划，重庆大学横向基金(No.104207520080834;NO.104207520080968)资助的项目 |
| Author Name | Affiliation | E-mail | | ZHANG Liangcai | Corresponding author. College of Mathematics and Physics, Chongqing University,
Chongqing 400044, China. | zlc213@163.com | | SHI Wujie | School of Mathematical Sciences, Suzhou University, Suzhou 215006, Jiangsu,
China. | wjshi@suda.edu.cn | | LIU Xuefeng | School of Materials Science and Engineering, University of Science and Technology
Beijing, Beijing 100083, China. | liuxuefengbj@163.com |
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| 中文摘要: |
| 令G是一个有限非交换群.如下定义群G的非交换图▽(G):其顶点集是G\Z(G),任意两个顶点x和y相连的充要条件是[x,y]≠1.2006年, Abdollahi A.,Akbari S.和Maimani H.R.提出了如下猜想:若群G满足条件▽(G)≌▽(M),其中M是有限非交换单群,则G≌M.尽管该猜想对于具有非连通素图的有限单群以及交错群A10足成立的,但是人们仍不知道它对于除A10外的具有连通素图的有限单群是否成立.该文证明了上述猜想对于射影特殊线性单群L4(4)也是成立的. |
| 英文摘要: |
| Let $G$ be a nonabelian group and associate a noncommuting graph
$\nabla(G)$ with $G$ as follows: The vertex set of $\nabla(G)$ is $G\backslash Z(G)$ with two
vertices $x$ and $y$ joined by an edge whenever the commutator of $x$ and $y$ is not
the identity.
In 2006, Abdollahi A., Akbari S. and Maimani H. R. put forward a conjecture called AAM's Conjecture %in \cite {AAM}
as follows: If $M$ is a finite nonabelian simple group and
$G$ is a group such that $\nabla(G)\cong \nabla (M)$, then $G\cong
M$. Even though this conjecture is known to hold
for all simple groups with nonconnected prime graphs and the alternating group $A_{10}$,
it is still unknown for
all simple groups with connected prime graphs except $A_{10}$.
It is proved that the conjecture is also true for the projective special
linear simple
group $L_{4}(4)$. |
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