论文标题
一种用于查找最小生成组有限基团的算法
An algorithm for finding minimal generating sets of finite groups
论文作者
论文摘要
在本文中，我们研究了Cayley Graph $ \ Mathrm {Cay}（g，a）$之间的连接，其中$ a $是组$ g $的任意子集，以及由$ a $产生的$ g $的子组的cosets。特别是，如果$ \ mathrm {cay}（g，a）$有限的组件有限，那么我们展示了如何构造$ g $的生成集。此外，我们提供了一种算法，用于使用其Cayley图来查找有限组的最小生成集。
In this article, we study connections between components of the Cayley graph $\mathrm{Cay}(G,A)$, where $A$ is an arbitrary subset of a group $G$, and cosets of the subgroup of $G$ generated by $A$. In particular, we show how to construct generating sets of $G$ if $\mathrm{Cay}(G,A)$ has finitely many components. Furthermore, we provide an algorithm for finding minimal generating sets of finite groups using their Cayley graphs.
