小阶群中NS-可补充子群

NS⁃supplemented Subgroups in Finite Groups of Small Order

在有限群中,子群的可补充性质对刻画群结构有重要影响。基于Monakhov等提出的NS-可补充子群的概念,从具体的群出发,研究了在3次对称群和4次对称群中的NS-可补充子群,并完全确定了其所有的NS-可补充子群。这也对NS-可补充子群的后续相关课题的研究起到积极的作用。

In finite groups,the supplementary properties of subgroups have a significant impact on characterizing group structures.Based on the concept of NS⁃supplemented subgroups proposed by Monakhov et al.,from the specific groups,NS⁃supplemented subgroups in the symmetric group of degree 3 and degree 4 were investigated,and all NS⁃supplemented sub⁃groups were completely identified.This result will play a positive role in the subsequent research on related topics of NS⁃supplemented subgroups.