Maximal irredundant families of minimal size in the alternating group

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

Strong approximation methods in group theory, an LMS/EPSRC Short course lecture notes

These are the lecture notes for the LMS/EPSRC short course on strong approximation methods in linear groups organized by Dan Segal in Oxford in September 2007.Comment: v4: Corollary 6.2 corrected, added a few small remark