论文标题
循环电力顺序的全体形状的正常亚组相互正常化
The mutually normalizing regular subgroups of the holomorph of a cyclic group of prime power order
论文作者
论文摘要
令$ g = c_ {p^n} $为有限的环状p组，让$ hol（g）$表示其Holomorph。在这项工作中，我们发现并表征了$ hol（g）$的常规亚组，这些子组在置换组$ sym（g）$中相互正常化。我们代表了图形顶点的常规亚组，当它们相互正常化时，我们将它们对通过边缘连接。构建此局部标准化图的方法取决于伽马功能的理论，最终结果将包含有关$ HOL（g）$的常规亚组的所有信息。
Let $G=C_{p^n}$ be a finite cyclic p-group, and let $Hol(G)$ denote its holomorph. In this work, we find and characterize the regular subgroups of $Hol(G)$ that are mutually normalizing each other in the permutation group $Sym(G)$. We represent such regular subgroups as vertices of a graph, and we connect a pair of them by an edge when they mutually normalize each other. The approach to construct this local normalizing graph relies on the theory of gamma functions, and the final result will contain all the information about the regular subgroups of $Hol(G)$ in a compact form.
