交换群的子群包含图的一些性质
Some Properties of Subgroup Inclusion Graph of an Abelian Group
DOI: 10.12677/PM.2023.137219, PDF,    科研立项经费支持
作者: 康富斌, 李元林*：江西理工大学理学院，江西 赣州
关键词: 群；交换群；子群包含图；子空间包含图；Groups； Abelian Groups； Subgroup Inclusion Graphs； Subspace Inclusion Graphs
摘要: 有限群G的子群包含图In(G)是指下列无向简单图：In(G)的顶点集是G的所有非平凡的子群组成的集合，而G的两个非平凡的子群H和K在In(G)中有边相连当且仅当H⊂K或H⊃K。本文将给出交换群的子群包含图的一些性质；特别地，本文将决定子群包含图是完美图(或三角图，或强三角图)的有限交换群。
Abstract: The subgroup inclusion graph In(G) of a finite group G is an undirected simple graph defined as follows: the vertex set of In(G) is consisting of all nontrivial subgroups of G, and for two nontrivial subgroups H and K of G, there is an edge adjoining them in In(G) if and only if H⊂K or H⊃K. In this paper, we will give some properties of the subgroup inclusion graph of Abelian groups; specially, we will determine the Abelian groups whose subgroup inclusion graph is a perfect graph (triangular graph, or strong triangular graph).
文章引用：康富斌, 李元林. 交换群的子群包含图的一些性质[J]. 理论数学, 2023, 13(7): 2120-2124. https://doi.org/10.12677/PM.2023.137219

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