偶阶子群是C-群的有限群  

Finite groups all of whose subgroups of even order are C-groups

作　　者：刘玉萍 卢家宽 张博儒 LIU Yuping;LU Jiakuan;ZHANG Boru(School of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《湘潭大学学报（自然科学版）》2023年第1期51-55,共5页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(11861015);广西自然科学基金项目(2020GXNSFAA238045);广西高校中青年教师科研基础能力提升项目(2020KY02019)。

摘　　要：称有限群G为C-群,如果对于■的任意因子d,G存在d阶的正规子群或反正规子群.该文主要研究偶阶子群是C-群的有限群.证明了每个偶阶极大子群皆为C-群的有限群是可解群,并给出了此类群的结构.此外,研究了每个偶阶二极大子群是C-群的非可解群.A group G is called a C-group if for each divisor d of the order of G,there exist a subgroup H of G of order d such that H is normal or abnormal in G.In this paper,we mainly investigate the structure of finite groups whose some proper subgroups of even order are C-groups.We prove the solvability of G when every maximal subgroups of even order are C-groups,The structure of this kind of group is given.Furthermore,we consider the non-solvable groups all of whose second maximal subgroups of even order are C-groups.

关 键 词：C-群 极大子群 可解群 

分 类 号：O152.1[理学—数学]