一个关于极大子群的迹的定理

One Theorem on Traces of Maximal Subgroups

众所周知,极大子群的性质与群结构有着紧密的联系。围绕一个迹的一个未解决问题,考虑了极大子群的迹的超可解性质对可解群的影响,得到了关于可解群的一个充分必要条件,为推进上述问题的解决做了积极的尝试。

The properties of maximal subgroups are closely related to the structure of groups. Focusing on an unsolved problem of a trace, the influence of the supersolvable property of the trace of a maximal subgroup on the solvable group is considered, and a necessity and sufficiency for the solvable group is obtained, which makes a positive attempt to promote the solution of the above problem.