论文标题
在增强功率图和通勤图之间
Between the enhanced power graph and the commuting graph
论文作者
论文摘要
本说明的目的是定义一个图形，其顶点集是有限的$ g $，其边缘集包含在$ g $的通勤图中，并包含$ g $的增强功率图。我们称此图为$ g $的深层通勤图。当且仅当其在$ g $通勤的每个中央扩展中，且仅当它们的反向图像中，$ g $的两个元素才会加入。 我们给出了该图的条件，使该图等于增强的功率图和通勤图，并表明$ g $的自动形态组充当了深层通勤图的自动形态。
The purpose of this note is to define a graph whose vertex set is a finite group $G$, whose edge set is contained in that of the commuting graph of $G$ and contains the enhanced power graph of $G$. We call this graph the deep commuting graph of $G$. Two elements of $G$ are joined in the deep commuting graph if and only if their inverse images in every central extension of $G$ commute. We give conditions for the graph to be equal to either of the enhanced power graph and the commuting graph, and show that the automorphism group of $G$ acts as automorphisms of the deep commuting graph.
