论文标题
在定向$ m $ -semiregular of有限群体的代表性上
On oriented $m$-semiregular representations of finite groups about valency two
论文作者
论文摘要
给定一个$ g $，{\ em $ M $ -M $ -CAYLEY DIGRAPH $ \ g $ of $ g $}是一个挖掘机，它具有一组自动形态，同构至$ g $ g $ semiregation semiregulary在带有$ m $ orbits的顶点套装上。我们说$ g $承认{\ em $ m $ -semiregular表示}（o $ m $ $ sr的简称），如果存在常规的$ m $ m $ -cayley-cayley digraph $ \ g $ over $ g $上的$ \ g $，以至于$ \ g $是$ \ g $的，并且其自动形状集团是与$ g $相同的。特别是，o $ 1 $ SR也被称为ORR。 Verret和Xia分类了有限的简单小组，在[ARS Math]中承认了价值二的ORR。当代。 22（2022），\＃P1.07]。令$ m \ geq 2 $为整数。在本文中，我们表明，最多两个要素产生的所有有限组都承认，价值$ $ m $ m $ sr除了四个小订单以外。因此，获得了有限简单的小组的分类，该小组承认获得了o $ m $ sr的价值。
Given a group $G$, an {\em $m$-Cayley digraph $\G$ over $G$} is a digraph that has a group of automorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$ orbits. We say that $G$ admits an {\em oriented $m$-semiregular representation} (O$m$SR for short), if there exists a regular $m$-Cayley digraph $\G$ over $G$ such that $\G$ is oriented and its automorphism group is isomorphic to $G$. In particular, O$1$SR is also named as ORR. Verret and Xia gave a classification of finite simple groups admitting an ORR of valency two in [Ars Math. Contemp. 22 (2022), \#P1.07]. Let $m\geq 2$ be an integer. In this paper, we show that all finite groups generated by at most two elements admit an O$m$SR of valency two except four groups of small orders. Consequently, a classification of finite simple groups admitting an O$m$SR of valency two is obtained.
