极小子群或正规或具有循环中心化子的有限群  

Finite Groups in Which Every Minimal Subgroup is Either Normal or Has Cyclic Centralizer

作　　者：任惠瑄 史江涛[1] REN Hui-xuan;SHI Jiang-tao(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1期17-19,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)。

摘　　要：为了进一步研究极小子群的中心化子对有限群结构的影响,应用反证法和极小阶反例的方法,刻画了每个极小子群或正规或具有循环中心化子的有限群的结构性质,证明了这类群如果非可解,则它们的每个2阶子群皆正规。In order to give a profound insight into the influence of the centralizer of minimal subgroups on the structure of finite groups,the methods of the proof by contradiction and the counterexample of the smallest order are applied to characterize the structural properties of a finite group in which every minimal subgroup is either normal or has cyclic centralizer,and it is proven that if such a group is non-solvable then its every subgroup of order 2 is normal.

关 键 词：极小子群 正规子群 循环子群 中心化子 P-幂零 

分 类 号：O152.1[理学—数学]