p-超循环嵌入子群的一个判别准则  

A Characterization of p-Hypercyclically Embedded Subgroups of Finite Groups

作　　者：张丽 郭文彬[2] 陈啸宇 ZHANG Li;GUO Wenbin;CHEN Xiaoyu(School of Mathematics and Physics,Anhui Jianzhu University,Hefei 230022.China;Corresponding author.School of Mathematics Sciences,University of Science and Technology of China,Hefei 230026,China;School of Mathematics Sciences,Nanjing Normal University.Nanjing 210022)

机构地区：[1]安徽建筑大学数理学院,合肥230022 [2]中国科学技术大学数学科学学院,合肥230026 [3]南京师范大学数学科学学院,南京210023

出　　处：《数学年刊（A辑）》2018年第3期297-308,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11771409);安徽建筑大学科研启动基金(No.K10807);南京师范大学科研启动基金(No.2015101XGQ0105)的资助

摘　　要：令E是有限群G的一个正规子群,且U是所有有限超可解群的集合.E称为在G中是p-超循环嵌入的,如果E的每个pd-阶的G-主因子是循环的.G的子群H称为在G中是U-Φ-可补充的,如果存在G的一个次正规子群T,使得G=HT,且(H∩T)H_G/H_G≤Φ/(H/H_G)Z_U(G/H_G),其中Z_U(G/H_G)是商群G/H_G的U-超中心.作者证明,如果E的一些p-子群在G中是U-Φ-可补充的,那么E在G中是p-超循环嵌入的.作为应用,得到了有限群是p-超可解的若干判断准则,并且推广了一些已知的结果.Let E be a normal subgroup of a finite group G and U the class of all finite super solvable groups. E is said to be p-hypercyclically embedded in G if every pd-G-chief factor below E is cyclic. A subgroup H of G is U-Φ-supplemented in G if there exists a subnormal subgroup T of G such that G =HT and（H∩T）H_G/H_G≤Φ（H/H_G）Z_U（G/H_G）,where Z_U（G/H_G） is the U-hypercentre of G/H_G In this paper, it is proved that E is phypercyclically embedded in G if some classes of p-subgroups of E are U-Φ-supplemented in G. As applications, some new characterizations of p-supersolvability of finite groups are obtained and some recent results are extended.

关 键 词：SYLOW P-子群 U-Φ-可补充子群 P-超可解群 P-幂零群 

分 类 号：O152[理学—数学]