| 有限群的$\Phi$-$\tau$-可补子群 |
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| 引用本文： | 马小箭,毛月梅.有限群的$\Phi$-$\tau$-可补子群[J].数学研究及应用,2017,37(3):281-289. |
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| 作者姓名： | 马小箭 毛月梅 |
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| 作者单位： | 山西大同大学数计学院, 山西 大同 037009,山西大同大学数计学院, 山西 大同 037009; 中国科学技术大学数学学院, 安徽 合肥 230026 |
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| 基金项目： | 国家自然科学基金 (Grant No.11371335). |
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| 摘 要： | 假设$\tau$是一个子群算子, $H$是有限群$G$的一个$p$-子群. 令 $\bar{G}=G/H_{G}$且$\bar{H}=H/H_{G}$, 如果$\bar{G}$有一个次正规子群$\bar{T}$ 和一个包含于$\bar{H}$ 的$\tau$-子群$\bar{S}$满足$\bar{G}=\bar{H}\bar{T}$且$\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$, 就称$H$是$G$的一个$\Phi$-$\tau$- 可补子群. 文章通过讨论群$G$的准素数子群的$\Phi$-$\tau$-可补性给出了超循环嵌入和$p$-幂零性的一些新的特征.
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| 关 键 词： | Sylow子群 次正规子群 子群算子 $p$-幂零群 $\Phi$-$\tau$-可补子群 |
| 收稿时间： | 2016/6/13 0:00:00 |
| 修稿时间： | 2016/12/7 0:00:00 |
On $\Phi$-$\tau$-Supplement Subgroups of Finite Groups |
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| Xiaojian MA and Yuemei MAO.On $\Phi$-$\tau$-Supplement Subgroups of Finite Groups[J].Journal of Mathematical Research with Applications,2017,37(3):281-289. |
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| Authors: | Xiaojian MA and Yuemei MAO |
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| Institution: | School of Mathematics and Computer, University of Datong of Shanxi, Shanxi 037009, P. R. China and School of Mathematics and Computer, University of Datong of Shanxi, Shanxi 037009, P. R. China; School of Mathematical Sciences, University of Science and Technology of China, Anhui 230026, P. R. China |
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| Abstract: | Let $\tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$. Let $\bar{G}=G/H_{G}$ and $\bar{H}=H/H_{G}$. We say that $H$ is $\Phi$-$\tau$-supplement in $G$ if $\bar{G}$ has a subnormal subgroup $\bar{T}$ and a $\tau$-subgroup $\bar{S}$ contained in $\bar{H}$ such that $\bar{G}=\bar{H}\bar{T}$ and $\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$. In this paper, some new characterizations of hypercyclically embedability and $p$-nilpotency of a finite group are obtained based on the assumption that some primary subgroups are $\Phi$-$\tau$-supplement in $G$. |
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| Keywords: | Sylow subgroups subnormal subgroups subgroup functor $p$-nilpotent group $\Phi$-$\tau$-supplement |
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