有限群的几乎SΦ-嵌入子群与群结构  

NEARLY SΦ-EMBEDDED SUBGROUPS AND THE STRUCTURE OF FINITE GROUPS

作　　者：霍丽君 朱清江 HUO Li-jun;ZHU Qing-jiang(College of Science,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《数学杂志》2025年第2期182-188,共7页Journal of Mathematics

基　　金：重庆市自然科学基金项目(CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575);重庆理工大学研究生教育高质量发展行动计划资助成果(gzljg2022319,gzlcx20243275).

摘　　要：本文利用有限群G中某些给定子群的几乎SΦ-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类的可解饱和群系的判别准则.In this paper,we investigate the structure of a finite group Gunder the assumption that some subgroups of G are nearly SΦ-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.

关 键 词：有限群 几乎SΦ-嵌入子群 SYLOW子群 P-幂零 超可解群 

分 类 号：O152.1[理学—数学]