| A Class of Generalized Nilpotent Groups |
| Received:March 30, 2009 Revised:January 18, 2010 |
| Key Words:
almost nilpotent inner-p-closed almost p-closed.
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| Fund Project:Supported by the Science Foundation of the Ministry of Education of China for the Returned Overseas Scholars (Grant No.2008101), the Science Foundation of Shanxi Province for the Returned Overseas Scholars (Grant No.200799) and the Doctoral Science Founda |
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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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.019 |
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