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| 摘要: |
| 本文研究了~Sylow~子群极大子群的局部~$SS$- 拟正规性对有限群结构的影响. 利用~Sylow $p$- 子群的少量局部~$SS$- 拟正规极大子群, 我们给出了有限群~$p$- 幂零性的若干新判据. 作为应用，我们得到了有限群属于包含超可解群类的饱和群系的若干充分条件. |
| 关键词: 有限群 极大子群 $p$-~幂零群 $SS$-~ 拟正规子群 |
| DOI： |
| 分类号:O152.1 |
| 基金项目: |
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| LOCAL $SS$-QUASINORMALITY OF SOME SUBGROUPS OF FINITE GROUPS |
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weihuaquan
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| Abstract: |
| This paper investigates the influence of local $SS$-quasinormal maximal subgroups of Sylow subgroups on the structure of finite groups. We present several new criteria on $p$-nilpotency of finite groups by utilizing a small quantity of local $SS$-quasinormal maximal subgroups of Sylow $p$-subgroups. As applications, we obtain some sufficient conditions for a finite group to be in a saturated formation containing the class of supersolvable groups. |
| Key words: finite group maximal subgroup $p$-nilpotent group $SS$-quasinormal group |
