Schmidt子群为Hall S-拟正规嵌入群的有限群  

On Finite Groups with Hall S-Quasinormally Embedded Schmidt Subgroups

作　　者：郑添尉 刘建军[1] ZHENG Tianwei;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）》2022年第9期19-22,共4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H是有限群G的子群.如果H为G的S-拟正规闭包H^(sqG)的Hall子群,则称H为G的一个Hall S-拟正规嵌入子群.如果一个非幂零有限群的任一真子群幂零,则称这个非幂零群为Schmidt群.该文证明了:如果有限群G的每一个Schmidt子群均为G中Hall S-拟正规嵌入子群,则G′幂零.A subgroup H of a finite group G is said to be Hall S-qusinormally embedded in G,if H is also a Hall subgroup of some S-quasinormal subgroup of G.A Schmidt group is a non-nilpotent finite group whose all proper subgroups are nilpotent.In this paper,it has been proved that if each Schmidt subgroup of a finite group G is Hall S-qusinormally embedded in G,then the derived subgroup G′is nilpotent.

关 键 词：Hall S-拟正规嵌入子群 Schmidt子群 幂零群 

分 类 号：O152.1[理学—数学]