论文标题
有限群体的定向$ m $ $ $ - 隔离表示
On oriented $m$-semiregular representations of finite groups
论文作者
论文摘要
如果存在有限的$ g $，则承认{\ em定期的定期表示}，如果存在$ g $的cayley digraph，以使其没有digons，并且其自动形态组是同构对$ g $。让$ m $成为一个积极的整数。在本文中，我们使用$ M $ -Cayley Digraphs将定向定期表示形式的概念扩展到定向$ m $ $ $ - 隔离表示。给定有限的$ g $，$ g $的{\ em $ m $ -M $ -CAYLEY DIGRAPH}是一个Digraph，它具有一组自动形态的同构至$ G $，以$ M $ ORBITS的顶点套件上的semiregulariand。我们说，如果存在常规的$ m $ m $ -m $ -cayley digraph $ g $的{\ em $ m $ $ -semiregular代表}，有限的组$ g $允许$ g $ $ g $，因此它没有digons，并且$ g $是对其自动形态群的同构。在本文中，我们对有限小组进行了分类，该小组承认每个正整数$ m $ a $ $ m $ m $ semiregular表示。
A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend the notion of oriented regular representations to oriented $m$-semiregular representations using $m$-Cayley digraphs. Given a finite group $G$, an {\em $m$-Cayley digraph} of $G$ is a digraph that has a group of automorphisms isomorphic to $G$ acting semiregularly on the vertex set with $m$ orbits. We say that a finite group $G$ admits an {\em oriented $m$-semiregular representation} if there exists a regular $m$-Cayley digraph of $G$ such that it has no digons and $G$ is isomorphic to its automorphism group. In this paper, we classify finite groups admitting an oriented $m$-semiregular representation for each positive integer $m$.
