论文标题
有限群的平等覆盖物
Equal Coverings of Finite Groups
论文作者
论文摘要
我们将探讨某些有限群体具有平等覆盖的何时以及有限群体没有的性质。不要与封面小组的概念相混淆，一个组的覆盖物是一组适当的亚组，其集合理论是原始组。我们将讨论掩护主题中研究的历史，并提及与平等掩护有关的概念中的一些发现，例如群体平等分区。我们开发了一些有用的定理，这些定理将有助于我们确定有限群体是否具有平等的覆盖率。另外，对于一个定理可能不完全有用，检查某个组时，我们将使用\ texttt {\ texttt {gap}}（组，算法，编程）进行计算参数。
We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose set-theoretic union is the original group. We will discuss the history of what has been researched in the topic of coverings, and as well as mention some findings in concepts related to equal coverings such as that of equal partition of a group. We develop some useful theorems that will aid us in determining whether a finite group has an equal covering or not. In addition, for when a theorem may not be entirely useful to examine a certain group we will turn to using \texttt{\texttt{GAP}} (Groups, Algorithms, Programming) for computational arguments.
