对称群S₃和S₄的c-可补充子群

c-Supplemented Subgroups in the Symmetry Groups S₃ and S₄

摘要: 在有限群中，子群的c-可补充性质对刻画群结构有着重要影响。这些性质比较抽象，因此找一些具体的例子对于理解这些性质至关重要。基于c-可补充子群的概念，本文从具体的3次对称群和4次对称群出发，研究了其子群的c-可补充性质，并完全确定了其所有的c-可补充子群。所得到的结论对探讨c-可补充子群的抽象性质和理论课题起到积极的作用。

Abstract: In finite groups, the c-supplemented properties of subgroups have a significant impact on characterizing group structures. These properties are relatively abstract, so finding specific examples is crucial for understanding these properties. Based on the concept of c-supplemented subgroups, this paper studies the c-complementary properties of subgroups from the symmetry groups of specific degrees 3 and 4, and completely determines all their c-complementary subgroups. The conclusions obtained have a positive impact on exploring the abstract properties and theoretical research of c-supplemented subgroups.