关于有限群的非循环真子群的自正规性和非正规性  

On Self-Normality and Non-Normality of Non-Cyclic Proper Subgroups of Finite Groups

作　　者：田云凤 史江涛[1] 刘文静 TIAN Yunfeng;SHI Jiangtao;LIU Wenjing(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2023年第3期274-276,共3页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11761079);山东省自然科学基金资助项目(ZR2017MA022,ZR2020MA044);烟台大学研究生科研创新基金资助。

摘　　要：为了进一步讨论非循环真子群的自正规性和非正规性之间的联系,通过分析相关的群结构,给出了一个直接的证明得到了有限群G的每个非循环真子群皆自正规当且仅当G为每个非循环真子群皆非正规的可解群。In order to give a further investigation of the relation between the self-normality and the normality of non-cyclic proper subgroups,we provide a direct proof that every non-cyclic proper subgroup of G is self-normalizing in G if and only if G is a solvable group in which every non-cyclic proper subgroup is non-normal by analyzing the structure of related groups.

关 键 词：有限群 非循环真子群 自正规性 非正规性 可解群 

分 类 号：O152.1[理学—数学]