| 摘要: |
| 本文研究了局部SS-拟正规极大子群对有限群结构的影响.利用Sylowp-子群的少量局部SS-拟正规极大子群,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:Supported by NSF of China (12061011) and NSF of Guangxi (2023GXNSFAA026333). |
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| LOCAL SS-QUASINORMALITY OF SOME SUBGROUPS OF FINITE GROUPS |
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WEI Hua-quan1, WU Hui1, HE Jia-wen2
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1.College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China;2.College of Artificial Intelligence and Software, Nanning University, Nanning 530200, China
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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 |
