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| 摘要: |
| 本文利用有限群~$G$ 中某些给定的子群的几乎~$S \Phi$-嵌入性质刻画了有限群的 ~$p$-幂零性, 得到有限群的新的结构特征.
此外, 还得到两个新的判断一个有限群是否属于给定包含超可解群构成的群类的可解饱和群系的两个判别准则. |
| 关键词: 有限群 几乎~$S \Phi$-嵌入子群 ~$Sylow$ 子群 ~$p$-幂零 超可解群 |
| DOI： |
| 分类号:O152.1 |
| 基金项目: |
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| NEARLY $S\Phi$-EMBEDDED SUBGROUPS AND THE STRUCTURE OF FINITE GROUPS |
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Huo Lijun
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| Abstract: |
| In this paper, we investigate the structure of a finite group $G$ under the assumption that some subgroups of $G$ are nearly $S\Phi$-embedded, and a new characterization of $p$-nilpotence of finite groups will be obtained. Moreover, we will obtain two criteria for a finite group to lie in a given solvably saturated formation containing the class of finite supersolvable groups. |
| Key words: finite group nearly $S\Phi$-embedded subgroup $Sylow$ subgroup $p$-nilpotent supersoluble group |
