| 梁登峰,施武杰.可解群的$\cd(G)-1$个特征标次数构成的图[J].数学研究及应用,2011,31(1):180~182 |
| 可解群的$\cd(G)-1$个特征标次数构成的图 |
| A Graph Associated with $|\cd(G)|-1$ Degrees of a Solvable Group |
| 投稿时间：2009-06-11 修订日期：2009-09-15 |
| DOI：10.3770/j.issn:1000-341X.2011.01.021 |
| 中文关键词: 可解群 不可约特征标次数. |
| 英文关键词:solvable groups irreducible character degrees. |
| 基金项目:国家自然科学基金资助项目(Grant No.10871032), 北京市属高校科技创新平台项目(Grant No.201098),教育部博士点资助项目(Grant No.20060285002). |
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| 中文摘要: |
| 令$G$是有限群.文中考虑集合$\cd(G)\backslash\{m\}$,其中 $m\in \cd(G)$.我们定义了图$\Delta(G-m)$,其顶点集合是$\rho(G-m)$,即由$\cd(G)\backslash\{m\}$中元素的素因子组成的集合.令$p,q\in\rho(G-m)$,如果$pq$整除$a\in \cd(G)\backslash\{m\}$中的某一个元素,我们就说$p$和$q$之间有一条边.文中证明了以下结果:若$G$是可解群,则$\Delta(G-m)$至多有两个连通分支. |
| 英文摘要: |
| Let $G$ be a group. We consider the set $\cd(G)\backslash\{m\}$, where $m\in \cd(G)$. We define the graph $\Delta(G-m)$ whose vertex set is $\rho(G-m)$, the set of primes dividing degrees in $\cd(G)\backslash\{m\}$. There is an edge between $p$ and $q$ in $\rho(G-m)$ if $pq$ divides a degree $a\in \cd(G)\backslash\{m\}$. We show that if $G$ is solvable, then $\Delta(G-m)$ has at most two connected components. |
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