一个关于可解群和极大子群的次正规迹的定理  

A Theorem on Solvable Groups and Subnormal Traces of Maximal Subgroups

作　　者：向艳辉 何金旅 

机构地区：[1]西华师范大学数学与信息学院,四川 南充

出　　处：《应用数学进展》2023年第6期2639-2642,共4页Advances in Applied Mathematics

摘　　要：极大子群是一类重要的子群,它的相关性质对描述群的结构起着重要的作用。结合子群的迹,并将群的极大子群进行分类,本文利用非交换的极大子群的迹的次正规性质来研究可解群,并得到了描述群的可解性的一个充分必要条件,将已有的结果进行了推广。As an important class of subgroups, the maximal subgroups play an important role in characteriz-ing the solvability of a group. In this paper, based on traces of subgroups and classifying the maxi-mal subgroups, we investigated the solvability of a group by using the subnormal property of the traces of nonabelian maximal subgroups and obtained a necessary and sufficient condition for characterizing solvable groups, which generalized the existing results.

关 键 词：极大子群 迹 次正规性 可解群 

分 类 号：O15[理学—数学]