Maximal irredundant families of minimal size in the alternating group. (English) Zbl 1515.20107
Summary: 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 \(\text{Mindim}(G)\) the minimal size of a maximal irredundant family of \(G\). In this paper we compute \(\text{Mindim}(G)\) when \(G\) is the alternating group on \(n\) letters.
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