Maximal irredundant families of minimal size in the alternating group

2018/08/13 by Martino Garonzi, Garonzi, Martino, Andrea Lucchini +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1808.04387

arxiv created 2019/04/09 · arxiv updated 2019/04/10

Abstract

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

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