论文标题
麦克劳林组的覆盖数和一些低度原始组
The Covering Numbers of the McLaughlin Group and some Primitive Groups of Low Degree
论文作者
论文摘要
组$ g $的A \ emph {有限封面是$ g $的适当子组的有限收集$ \ mathcal {c} $，属于$ \ bigcup \ bigcup \ mathcal {c} = g $的属性。当且仅当它是非周期时，有限组就可以承认有限的盖子。更普遍的是，众所周知，只有当它具有有限的非循环同构图像时，一组会允许有限的盖子。如果$ \ Mathcal {c} $是组$ g $的有限封面，而没有$ g $的封面，则存在较少的子组，则$ \ nathcal {c} $被认为是$ g $的\ emph {math cover} $ g $的最小值，$ g $，$ \ nathcal $ demcal a coper n of Covel n of Covel as coper of Cover of Cover of Cover of Cover of Cover of of coper of of coper { $σ（g）$。在这里，我们研究了麦克劳克林零星简单组和一些低度原始组的覆盖数。
A \emph{finite cover} of a group $G$ is a finite collection $\mathcal{C}$ of proper subgroups of $G$ with the property that $\bigcup \mathcal{C} = G$. A finite group admits a finite cover if and only if it is noncyclic. More generally, it is known that a group admits a finite cover if and only if it has a finite, noncyclic homomorphic image. If $\mathcal{C}$ is a finite cover of a group $G$, and no cover of $G$ with fewer subgroups exists, then $\mathcal{C}$ is said to be a \emph{minimal cover} of $G$, and the cardinality of $\mathcal{C}$ is called the \emph{covering number} of $G$, denoted by $σ(G)$. Here we investigate the covering numbers of the McLaughlin sporadic simple group and some low degree primitive groups.
