某些子群介于正规与反正规之间的有限群  

Finite Groups in Which Certain Subgroups are Between Normal and Abnormal

作　　者：郭鹏飞[1] 石化国[2] Peng Fei GUO;Hua Guo SHI(School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,P.R.China;Department of Teacher Education,Sichuan Vocational and Technical College,Suining 629000,P.R.China)

机构地区：[1]海南师范大学数学与统计学院,海口571158 [2]四川职业技术学院教师教育系,遂宁629000

出　　处：《数学学报（中文版）》2022年第5期841-848,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12061030,11661031);海南省自然科学基金资助项目(119MS039)。

摘　　要：有限群G的子群H称为G的BNA子群,若对任意的x∈G有H^(x)=H或x∈<H,H^(x)>.若有限群G的所有素数阶和4阶循环子群都是G的BNA子群,则称G为CBNA群.本文主要刻画CBNA群的结构,并且给出所有真子群都是CBNA群的完全分类.A subgroup H of a finite group G is a BNA-subgroup of G if either H^(x)=H or ∈(H,H^(x))for all x ∈ G.A finite group G is called a CBNA-group if its all cyclic subgroups of order prime or 4 are BNA-subgroups of G.The main aim of this paper is to investigate the structure of CBNA-groups,and the groups whose all proper subgroups are CBNA-groups are classified completely。

关 键 词：BNA子群 极小子群 循环子群 超可解群 CBNA群 

分 类 号：O152.1[理学—数学]