| 余大鹏,张良才.L7（3）与GL7（3）的OD-刻画[J].数学年刊A辑,2012,33(5):599~608 |
| L7（3）与GL7（3）的OD-刻画 |
| OD-Characterization of L7（3） and GL7（3） |
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| DOI： |
| 中文关键词: 有限单群 素图 顶点度数 素图度数序列 |
| 英文关键词:Finite simple group, Prime graph, Degree of a vertex, Degree
pattern |
| 基金项目:国家自然科学基金(No11171364);国家杰出青年基金(No11001226);重庆市科委自然科学基金计划(No2010BB9206);重庆市教委2011年度科学技术研究项目(NoKJ111207);重庆文理学院2010年校级科研项目(NoZ2010ST15)资助的项目 |
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| 中文摘要: |
| 对于任意一个有限群G,令π（G）表示由它的阶的所有素因子构成的集合.构建一种与之相关的简单图,称之为素图,记作Γ（G）.该图的顶点集合是π（G）,图中两顶点p,g相连（记作p～q）的充要条件是群G恰有pq阶元.设π（G）={P1,p2,…,px}.对于任意给定的p∈π（G）,令deg（p）:=|{q∈π（G）|在素图Γ（G）中,p～q}|,并称之为顶点p的度数.同时,定义D（G）:=（deg（p1）,deg（p2）,…,deg（ps））,其中p12<… |
| 英文摘要: |
| If $G$ is a finite group, we denote by $\pi(G)$ the set of all the prime factors of the
order of $G$' and construct a simple graph $\Gamma(G)$, called the prime graph of $G$, as follows.
The vertices of $\Gamma(G)$ are $\pi(G)$ and two distinct vertices $p$, $q$ are joined by an
edge, denoted by $p\sim q$, if and only if there is an element of order
$pq$ in $G$.
For any given $p\in \pi(G)=\{p_{1}, p_{2},\cdots , p_{s}\}$,
define ${\rm deg}(p):=|\{q\in \pi(G)\mid q\sim p \ \text{in} \ \Gamma(G)\}|$, which is called the
degree of $p$. Define $D(G):=({\rm deg}(p_{1}), {\rm deg}(p_{2}),
\cdots,{\rm deg}(p_{s}))$, where $p_{1} |
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