偶数阶极大子群均为CBNA-子群的有限群  

Finite Groups with Even Order Maximal Subgroups are CBNA-Subgroups

作　　者：唐康 刘建军[1] TANG Kang;LIU Jianjun(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2023年第2期23-27,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971391);中央高校基本科研业务费项目(XDJK2020B052).

摘　　要：设G为有限群,H为G的子群.如果对任意的x∈G有H^(x)=H或x∈〈H,H^(x)〉,则称H为G的BNA-子群.如果有限群G的所有极小子群和4阶循环子群均为G的BNA-子群,则称G为CBNA-群.本文刻画了所有偶数阶极大子群均为CBNA-群,而群本身是一个偶数阶非CBNA-群的群结构.A subgroup H of a finie group G is said to be a BNA-subgroup of G if either H^(x)=H or x∈〈H,H^(x)〉for each x∈G.A finite group G is called a CBNA-group if every minimal subgroup and cyclic subgroup of order 4 of G is a BNA-subgroup of G.In this paper,we characterize that every maximal subgroup of even order is a CBNA-groups,and the group itself is a group structure of non-CBNA-groups of even order.

关 键 词：BNA-子群 CBNA-群 偶数阶极大子群 极小非CBNA-群 

分 类 号：O152.1[理学—数学]