| Finite Groups with Some Subgroups Weakly $s$-Permutably Embedded |
| Received:November 22, 2013 Revised:April 17, 2014 |
| Key Words:
finite groups weakly $s$-permutably embedded subgroups $p$-nilpotent groups $p$-supersolvable groups supersolvable groups.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11201082; 11171353), China Postdoctoral Science Foundation (Grant No.2013T60866), the Natural Science Foundation of Guangdong Province (Grant No.S201204007267) and Outstanding Young Teachers Training Project of Guangdong Province (Grant No.Yq2013061). |
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| Abstract: |
| Let $P$ be a Sylow $p$-subgroup of a group $G$ with the smallest generator number $d$, where $p$ is a prime. Denote by $\cal M$$_d(P)=\{P_1,P_2,\ldots,P_d\}$ a set of maximal subgroups of $P$ such that $\Phi(P)=\cap^{d}_{n=1}P_n$. In this paper, we investigate the structure of a finite group $G$ under the assumption that the maximal subgroups in $\cal M$$_d(P)$ are weakly $s$-permutably embedded in $G$, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly $s$-permutably embedded subgroups. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.05.004 |
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