| 可解群的$\cd(G)-1$个特征标次数构成的图 |
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| 引用本文： | 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. |
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| 作者姓名： | 梁登峰 施武杰 |
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| 作者单位： | 北京工商大学计算机与信息工程学院, 北京 100048;苏州大学数学系, 江苏 苏州 215006 |
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| 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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| 摘 要： | Let G be a group. We consider the set cd（G）／{m}, where m ∈ cd（G）. We define the graph △（G - m） whose vertex set is p（G - m）, the set of primes dividing degrees in cd（G）／{m}. There is an edge between p and q in p（G - m） ifpq divides a degree a ∈ cd（G）／{m}. We show that if G is solvable, then △（G - m） has at most two connected components.
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| 关 键 词： | solvable groups irreducible character degrees. |
| 收稿时间： | 2009/6/11 0:00:00 |
| 修稿时间： | 2009/9/15 0:00:00 |
A Graph Associated with $|\cd(G)|-1$ Degrees of a Solvable Group |
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| Deng Feng LIANG and Wu Jie SHI.A Graph Associated with $|\cd(G)|-1$ Degrees of a Solvable Group[J].Journal of Mathematical Research with Applications,2011,31(1):180-182. |
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| Authors: | Deng Feng LIANG and Wu Jie SHI |
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| Institution: | 1. College of Computer and Information Engineering,Beijing Technology and Business University,Beijing 100048,P.R.China;Department of Mathematics,Suzhou University,Jiangsu 215006,P.R.China
2. Department of Mathematics,Suzhou University,Jiangsu 215006,P.R.China |
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| Abstract: | 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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| Keywords: | solvable groups irreducible character degrees |
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