论文标题
关于与正常子组的共轭类大小相关的图表的规律性
On the regularity of a graph related to conjugacy class sizes of a normal subgroup
论文作者
论文摘要
给定一个有限的组$ g $，带有普通子组$ n $，简单的图$γ_\ textit {g}（\ textit {n}）$是一个图形，其顶点为$ | x^g | $，其中$ x \ en $ x \ in {n \ setMinus {z（g）} $ n $ x $ n是$ x^$ n是$ x^ug- $ x $。两个顶点$ | x^g | $和$ | y^g | $如果它们不是共同奖励，则相邻。在本文中，我们证明，如果$γ_g（n）$是连接不完整的常规图，则$ n = p \ times {a} $，其中$ p $是$ p $ -group，对于某些prime $ p $和$ p $和$ a \ leq a \ leq {z（g）} $，以及$ {\ bf z} $ {\ bf z}（n）（n）（n）（n）\ k）
Given a finite group $G$ with a normal subgroup $N$, the simple graph $Γ_\textit{G}( \textit{N} )$ is a graph whose vertices are of the form $|x^G|$, where $x\in{N\setminus{Z(G)}}$, and $x^G$ is the $G$-conjugacy class of $N$ containing the element $x$. Two vertices $|x^G|$ and $|y^G|$ are adjacent if they are not co-prime. In this article we prove that, if $Γ_G(N)$ is a connected incomplete regular graph, then $N= P \times{A}$ where $P$ is a $p$-group, for some prime $p$ and $A\leq{Z(G)}$, and ${\bf Z}(N)\not = N\cap {\bf Z}(G)$.
