The Covering Numbers of ${\mathbb{A}}_9$ and ${\mathbb{A}}_{11}$

Abstract

A collection $\mathcal{S}$ of proper subgroups of a group $G$ is said to be a cover (or covering) for $G$ if the union of the members of $\mathcal{S}$ is all of $G$. A cover $\mathcal{C}$ of minimal cardinality is called a minimal cover for $G$ and $|\mathcal{C}|$ is called the covering number of $G$, denoted by $\sigma (G)$. In this paper we determine the covering numbers of the alternating groups $A_9$ and $A_{11}$.