An algorithm for finding minimal generating sets of finite groups
نویسندگان
1 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
doi
10.22034/as.2021.2029چکیده
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.
