McLaughlin群和某些低次本原群的覆盖数
The Covering Numbers of the McLaughlin Group and some Primitive Groups of Low Degree
摘要：
群$G$的\emph{finite cover}是$G$的真子群的有限集合$\mathcal{C}$，其性质为$\bigcup \mathcal{C} = G$。有限群允许有限覆盖当且仅当它是非循环的。更一般地说，已知一个群允许有限覆盖当且仅当它有一个有限的非循环同态像。如果$\mathcal{C}$是群$G$的有限覆盖，并且不存在具有较少子群的$G$的覆盖，则称$\mathcal{C}$是$G$的\emph{minimal cover}，并且$\mathcal{C}$的基数称为$G$的\emph{covering number}，用$σ(G)$表示。本文研究了McLaughlin散在单群和一些低次本原群的覆盖数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
