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.
Categories: math.GR