{"paper":{"title":"Maximal irredundant families of minimal size in the alternating group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrea Lucchini, Martino Garonzi","submitted_at":"2018-08-13T18:14:05Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04387","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}