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
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。
Abstract:
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.
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