Maximal irredundant families of minimal size in the alternating group

Abstract

Let $G$ be a finite group. A family $\mathcal{M}$ of maximal subgroups of $G$ is called `irredundant' if its intersection is not equal to the intersection of any proper subfamily. $\mathcal{M}$ is called `maximal irredundant' if $\mathcal{M}$ is irredundant and it is not properly contained in any other irredundant family. We denote by \mbox{Mindim}(G) the minimal size of a maximal irredundant family of $G$. In this paper we compute \mbox{Mindim}(G) when $G$ is the alternating group on $n$ letters