论文标题
$ \ mathrm {pgl} _n（\ mathbb {f} _Q）$的减少电源图
Reduced Power Graphs of $\mathrm{PGL}_n(\mathbb{F}_q)$
论文作者
论文摘要
给定一个$ g $，当一个且仅当一个是另一个力量时，让我们通过边缘连接两个非身份元素。这给出了$ g $减去身份的图形结构，称为还原功率图。 Akbari和Ashrafi的猜想是，如果非亚洲有限的简单组具有连接的减少功率图，则必须是交替组。 在本文中，我们将全面描述何时$ \ mathrm {pgl} _n（\ Mathbb {f} _Q）$的功率图何时连接了所有$ q $以及所有$ n \ geq 3 $。特别是，Akbari和Ashrafi的猜想是错误的。我们还将在其直径上提供上限，并在断开连接时提供所有连接组件的描述。
Given a group $G$, let us connect two non-identity elements by an edge if and only if one is a power of another. This gives a graph structure on $G$ minus identity, called the reduced power graph. It is conjectured by Akbari and Ashrafi that if a non-abelian finite simple group has a connected reduced power graph, then it must be an alternating group. In this paper, we shall give a complete description of when the reduced power graphs of $\mathrm{PGL}_n(\mathbb{F}_q)$ are connected for all $q$ and all $n\geq 3$. In particular, the conjectured by Akbari and Ashrafi is false. We shall also provide an upper bound in their diameters, and in case of disconnection, provide a description of all connected components.
