| 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 |
| 一类广义幂零群 |
| A Class of Generalized Nilpotent Groups |
| 投稿时间：2009-03-30 修订日期：2010-01-18 |
| DOI：10.3770/j.issn:1000-341X.2011.02.019 |
| 中文关键词: 几乎幂零 内p-闭 几乎p-闭. |
| 英文关键词:almost nilpotent inner-p-closed almost p-closed. |
| 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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| 中文摘要: |
| 本文研究这样一类群,其包含真子群$H_1$, $H_2$使得其它任何不包含在它们中的真子群均为$p$-闭的,并获得:若该群可解,则其阶所含素因子个数在2到4之间;若不可解,则其为形如: $\langle x\rangle\ltimes N$的群,其中$N/\phi(N)$为非交换单群.在一定条件下本文还决定了几乎2-闭群的结构. |
| 英文摘要: |
| 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 $H_1\cup H_2$ 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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