| 一类广义幂零群 |
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| 引用本文： | 李千路,李秀兰,毛月梅.一类广义幂零群[J].数学研究及应用,2011,31(2):347-352. |
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| 作者姓名： | 李千路 李秀兰 毛月梅 |
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| 作者单位： | 山西大同大学数学系, 山西 大同 037009;山西大同大学数学系, 山西 大同 037009;山西大同大学数学系, 山西 大同 037009 |
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| 基金项目： | 教育部留学归国基金(Grant No.2008101),山西省留学归国基金(Grant No.200799)及山西大同大学博士基金(Grant No.2008-B-02). |
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| 摘 要： | This paper considers such a group G which possesses nontrivial proper subgroups H 1 ,H 2 such that any proper subgroup of G not contained in H 1 ∪ H 2 is p-closed and obtains that if G is soluble,then the number of prime divisors contained in ｜G｜ is 2,3 or 4;if not,then it has a form x N where N/Φ（N） is a non-abelian simple group.Then the structure of such a group is determined for p = 2,H 1 = H 2 under some conditions.
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| 关 键 词： | almost nilpotent inner-p-closed almost p-closed |
| 收稿时间： | 2009/3/30 0:00:00 |
| 修稿时间： | 2010/1/18 0:00:00 |
A Class of Generalized Nilpotent Groups |
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| Qian Lu LI,Xiu Lan LI and Yue Mei MAO.A Class of Generalized Nilpotent Groups[J].Journal of Mathematical Research with Applications,2011,31(2):347-352. |
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| Authors: | Qian Lu LI Xiu Lan LI and Yue Mei MAO |
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| Institution: | Department of Mathematics, Shanxi Datong University, Shanxi 037009, P. R. China |
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| Abstract: | This paper considers such a group $G$ which possesses nontrivial proper subgroups $H_1$, $H_2$ such that any proper subgroup of $G$ not contained in $H_1\cup H_2$ is $p$-closed and obtains that if $G$ is soluble, then the number of prime divisors contained in $|G|$ is $2, 3$ or $4$; if not, then it has a form $\langle x \rangle\ltimes N$ where $N/\Phi(N)$ is a non-abelian simple group. Then the structure of such a group is determined for $p=2$, $H_1=H_2$ under some conditions. |
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| Keywords: | almost nilpotent inner-p-closed almost p-closed |
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