论文标题
零星群体的新特征
A New Characterization of Sporadic Groups
论文作者
论文摘要
让$ g $为有限的组，$ n $ a正整数。 $π（n）$表示$ n $和$π（g）=π（| g |）$的所有素数组的集合。由Grenberg和Kegel定义的Prime Graph $γ（g）$ $ G $是一个图形，其顶点套件为$π（g）$，两个dertices $ p，\ q $ in $π（g）$ in $ g $ in Edge of Edge且仅当$ G $包含订单$ PQ $的元素时。在本文中，获得了零星简单组的新特征，也就是说，如果$ g $是有限的组，而零星简单组的$ s $。然后，仅当$ g \ cong s $时，仅当$ | g | = | s | $和$γ（g）$被断开连接。这种表征统一了可以得出结论的几种特征，该组具有非连接的质量图，因此，零星简单组的几个已知特征成为这种新特征的推论。
Let $G$ be a finite group, $n$ a positive integer. $π(n)$ denotes the set of all prime divisors of $n$ and $π(G)=π(|G|)$. The prime graph $Γ(G)$ of $G$, defined by Grenberg and Kegel, is a graph whose vertex set is $π(G)$, two vertices $p,\ q$ in $π(G)$ joined by an edge if and only if $G$ contains an element of order $pq$. In this article, a new characterization of sporadic simple groups is obtained, that is, if $G$ is a finite group and $S$ a sporadic simple group. Then $G\cong S$ if and only if $|G|=|S|$ and $Γ(G)$ is disconnected. This characterization unifies the several characterizations that can conclude the group has non-connected prime graphs, hence several known characterizations of sporadic simple groups become the corollaries of this new characterization.
